Pub Date : 2025-12-24DOI: 10.1016/j.spa.2025.104857
Chiara Amorino , Ivan Nourdin , Radomyra Shevchenko
We address the problem of estimating the drift parameter in a system of N interacting particles driven by additive fractional Brownian motion of Hurst index H ≥ 1/2. Considering continuous observation of the interacting particles over a fixed interval [0, T], we examine the asymptotic regime as N → ∞. Our main tool is a random variable reminiscent of the least squares estimator but unobservable due to its reliance on the Skorohod integral. We demonstrate that this object is consistent and asymptotically normal by establishing a quantitative propagation of chaos for Malliavin derivatives, which holds for any H ∈ (0, 1). Leveraging a connection between the divergence integral and the Young integral, we construct computable estimators of the drift parameter. These estimators are shown to be consistent and asymptotically Gaussian. Finally, a numerical study highlights the strong performance of the proposed estimators.
{"title":"Fractional interacting particle system: Drift parameter estimation via Malliavin calculus","authors":"Chiara Amorino , Ivan Nourdin , Radomyra Shevchenko","doi":"10.1016/j.spa.2025.104857","DOIUrl":"10.1016/j.spa.2025.104857","url":null,"abstract":"<div><div>We address the problem of estimating the drift parameter in a system of <em>N</em> interacting particles driven by additive fractional Brownian motion of Hurst index <em>H</em> ≥ 1/2. Considering continuous observation of the interacting particles over a fixed interval [0, <em>T</em>], we examine the asymptotic regime as <em>N</em> → ∞. Our main tool is a random variable reminiscent of the least squares estimator but unobservable due to its reliance on the Skorohod integral. We demonstrate that this object is consistent and asymptotically normal by establishing a quantitative propagation of chaos for Malliavin derivatives, which holds for any <em>H</em> ∈ (0, 1). Leveraging a connection between the divergence integral and the Young integral, we construct computable estimators of the drift parameter. These estimators are shown to be consistent and asymptotically Gaussian. Finally, a numerical study highlights the strong performance of the proposed estimators.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"195 ","pages":"Article 104857"},"PeriodicalIF":1.2,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145886101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-23DOI: 10.1016/j.spa.2025.104854
Luisa Beghin , Nikolai Leonenko , Ivan Papić , Jayme Vaz
We define a novel class of time-changed Pearson diffusions, termed stretched non-local Pearson diffusions, where the stochastic time-change model has the Kilbas-Saigo function as its Laplace transform. Moreover, we introduce a stretched variant of the Caputo fractional derivative and prove that its eigenfunction is, in fact, the Kilbas-Saigo function. Furthermore, we solve fractional Cauchy problems involving the generator of the Pearson diffusion and the Fokker-Planck operator, providing both analytic and stochastic solutions, which connect the newly defined process and fractional operator with the Kilbas-Saigo function. We also prove that stretched non-local Pearson diffusions share the same limiting distributions as their standard counterparts. Finally, we investigate fractional hyperbolic Cauchy problems for Pearson diffusions, which resemble time-fractional telegraph equations, and provide both analytical and stochastic solutions. As a byproduct of our analysis, we derive a novel representation and an asymptotic formula for the Kilbas-Saigo function with complex arguments, which, to the best of our knowledge, are not currently available in the existing literature.
{"title":"Stretched non-local Pearson diffusions","authors":"Luisa Beghin , Nikolai Leonenko , Ivan Papić , Jayme Vaz","doi":"10.1016/j.spa.2025.104854","DOIUrl":"10.1016/j.spa.2025.104854","url":null,"abstract":"<div><div>We define a novel class of time-changed Pearson diffusions, termed stretched non-local Pearson diffusions, where the stochastic time-change model has the Kilbas-Saigo function as its Laplace transform. Moreover, we introduce a stretched variant of the Caputo fractional derivative and prove that its eigenfunction is, in fact, the Kilbas-Saigo function. Furthermore, we solve fractional Cauchy problems involving the generator of the Pearson diffusion and the Fokker-Planck operator, providing both analytic and stochastic solutions, which connect the newly defined process and fractional operator with the Kilbas-Saigo function. We also prove that stretched non-local Pearson diffusions share the same limiting distributions as their standard counterparts. Finally, we investigate fractional hyperbolic Cauchy problems for Pearson diffusions, which resemble time-fractional telegraph equations, and provide both analytical and stochastic solutions. As a byproduct of our analysis, we derive a novel representation and an asymptotic formula for the Kilbas-Saigo function with complex arguments, which, to the best of our knowledge, are not currently available in the existing literature.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"195 ","pages":"Article 104854"},"PeriodicalIF":1.2,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145847611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-23DOI: 10.1016/j.spa.2025.104856
Gustavo O. De Carvalho, Fábio P. Machado
We study the frog model on with geometric lifetimes, introducing a random survival parameter. Active and inactive particles are placed at the vertices of . The lifetime of each active particle follows a geometric random variable with parameter , where p is randomly sampled from a distribution π. Each active particle performs a simple random walk on until it dies, activating any inactive particles it encounters along its path. In contrast to the usual case where p is fixed, we show that there exist non-trivial distributions π for which the model survives with positive probability. More specifically, for π ∼ Beta(α, β), we establish the existence of a critical value , that separates almost sure extinction from survival with positive probability. Furthermore, we show that the model is recurrent whenever it survives with positive probability.
{"title":"Frog model on Z with random survival parameter","authors":"Gustavo O. De Carvalho, Fábio P. Machado","doi":"10.1016/j.spa.2025.104856","DOIUrl":"10.1016/j.spa.2025.104856","url":null,"abstract":"<div><div>We study the frog model on <span><math><mi>Z</mi></math></span> with geometric lifetimes, introducing a random survival parameter. Active and inactive particles are placed at the vertices of <span><math><mi>Z</mi></math></span>. The lifetime of each active particle follows a geometric random variable with parameter <span><math><mrow><mn>1</mn><mo>−</mo><mi>p</mi></mrow></math></span>, where <em>p</em> is randomly sampled from a distribution <em>π</em>. Each active particle performs a simple random walk on <span><math><mi>Z</mi></math></span> until it dies, activating any inactive particles it encounters along its path. In contrast to the usual case where <em>p</em> is fixed, we show that there exist non-trivial distributions <em>π</em> for which the model survives with positive probability. More specifically, for <em>π</em> ∼ <em>Beta</em>(<em>α, β</em>), we establish the existence of a critical value <span><math><mrow><mi>β</mi><mo>=</mo><mn>0.5</mn></mrow></math></span>, that separates almost sure extinction from survival with positive probability. Furthermore, we show that the model is recurrent whenever it survives with positive probability.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"194 ","pages":"Article 104856"},"PeriodicalIF":1.2,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145842462","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-20DOI: 10.1016/j.spa.2025.104853
Dirk Erhard , Julien Poisat
In this paper we introduce a topology under which the pair empirical measure of a large class of random walks satisfies a strong Large Deviation principle. The definition of the topology is inspired by the recent article by Mukherjee and Varadhan [1]. This topology is natural for translation-invariant problems such as the downward deviations of the volume of a Wiener sausage or simple random walk, known as the Swiss cheese model [2]. We also adapt our result to some rescaled random walks and provide a contraction principle to the single empirical measure despite a lack of continuity from the projection map, using the notion of diagonal tightness.
{"title":"Strong large deviation principles for pair empirical measures of random walks in the Mukherjee-Varadhan topology","authors":"Dirk Erhard , Julien Poisat","doi":"10.1016/j.spa.2025.104853","DOIUrl":"10.1016/j.spa.2025.104853","url":null,"abstract":"<div><div>In this paper we introduce a topology under which the pair empirical measure of a large class of random walks satisfies a strong Large Deviation principle. The definition of the topology is inspired by the recent article by Mukherjee and Varadhan [1]. This topology is natural for translation-invariant problems such as the downward deviations of the volume of a Wiener sausage or simple random walk, known as the Swiss cheese model [2]. We also adapt our result to some rescaled random walks and provide a contraction principle to the single empirical measure despite a lack of continuity from the projection map, using the notion of diagonal tightness.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"194 ","pages":"Article 104853"},"PeriodicalIF":1.2,"publicationDate":"2025-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145842464","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-15DOI: 10.1016/j.spa.2025.104851
Arnaud Guillin , Boris Nectoux , Liming Wu
In this work, we investigate the ergodic behavior of a system of particules, subject to collisions, before it exits a fixed subdomain of its state space. This system is composed of several one-dimensional ordered Brownian particules in interaction with electrostatic repulsions, which is usually referred as the (generalized) Dyson Brownian motion. The starting points of our analysis are the work [E. Cépa and D. Lépingle, 1997 Probab. Theory Relat. Fields] which provides existence and uniqueness of such a system subject to collisions via the theory of multivalued SDEs and a Krein-Rutman type theorem derived in [A. Guillin, B. Nectoux, L. Wu, 2020 J. Eur. Math. Soc.].
{"title":"Quasi-stationarity of the Dyson Brownian motion with collisions","authors":"Arnaud Guillin , Boris Nectoux , Liming Wu","doi":"10.1016/j.spa.2025.104851","DOIUrl":"10.1016/j.spa.2025.104851","url":null,"abstract":"<div><div>In this work, we investigate the ergodic behavior of a system of particules, subject to collisions, before it exits a fixed subdomain of its state space. This system is composed of several one-dimensional ordered Brownian particules in interaction with electrostatic repulsions, which is usually referred as the (generalized) Dyson Brownian motion. The starting points of our analysis are the work [E. Cépa and D. Lépingle, 1997 Probab. Theory Relat. Fields] which provides existence and uniqueness of such a system subject to collisions via the theory of multivalued SDEs and a Krein-Rutman type theorem derived in [A. Guillin, B. Nectoux, L. Wu, 2020 J. Eur. Math. Soc.].</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"193 ","pages":"Article 104851"},"PeriodicalIF":1.2,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-13DOI: 10.1016/j.spa.2025.104852
B. Li , M.A. Lkabous , J.M. Pedraza
This paper investigates the optimal prediction of the last r-excursion time for a Brownian motion model. The last r-excursion time, denoted by lr, refers to the right endpoint of the last negative excursion lasting longer than a constant r > 0. It reduces to the standard last passage time when r↓0. For a Brownian motion with drift μ > 0 and volatility σ > 0, our goal is to identify an optimal stopping time that minimizes the (L1) distance from the last r-excursion time lr. We find that the optimal stopping barrier exhibits two distinct structures: a constant barrier (characterized as a solution of a non-linear equation) or a moving barrier (characterized by the unique solution to an integral equation) depending on the ratio which integrates a firm’s financial profitability, volatility, and risk tolerance to financial distress. To obtain the optimal stopping time, we examine the smooth fit condition, Lipschitz continuity of the barrier, and probability regularity of the boundary points. As an application in risk management, we develop a decision rule that informs the timing of business expansion and contraction.
{"title":"Optimal prediction of the last r-excursion time of Brownian motion models","authors":"B. Li , M.A. Lkabous , J.M. Pedraza","doi":"10.1016/j.spa.2025.104852","DOIUrl":"10.1016/j.spa.2025.104852","url":null,"abstract":"<div><div>This paper investigates the optimal prediction of the last <em>r</em>-excursion time for a Brownian motion model. The last <em>r</em>-excursion time, denoted by <em>l<sub>r</sub></em>, refers to the right endpoint of the last negative excursion lasting longer than a constant <em>r</em> > 0. It reduces to the standard last passage time when <em>r</em>↓0. For a Brownian motion with drift <em>μ</em> > 0 and volatility <em>σ</em> > 0, our goal is to identify an optimal stopping time that minimizes the (<em>L</em><sub>1</sub>) distance from the last <em>r</em>-excursion time <em>l<sub>r</sub></em>. We find that the optimal stopping barrier exhibits two distinct structures: a constant barrier (characterized as a solution of a non-linear equation) or a moving barrier (characterized by the unique solution to an integral equation) depending on the ratio <span><math><mrow><mi>R</mi><mo>=</mo><mfrac><mrow><mi>μ</mi><msqrt><mi>r</mi></msqrt></mrow><mi>σ</mi></mfrac></mrow></math></span> which integrates a firm’s financial profitability, volatility, and risk tolerance to financial distress. To obtain the optimal stopping time, we examine the smooth fit condition, Lipschitz continuity of the barrier, and probability regularity of the boundary points. As an application in risk management, we develop a decision rule that informs the timing of business expansion and contraction.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"194 ","pages":"Article 104852"},"PeriodicalIF":1.2,"publicationDate":"2025-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145814323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-13DOI: 10.1016/j.spa.2025.104850
Jiaqi Wang, Gennady Samorodnitsky
How do large deviation events in a stationary process cluster? The answer depends not only on the type of large deviations, but also on the length of memory in the process. Somewhat unexpectedly, it may also depend on the tails of the process. In this paper we work in the context of large deviations for partial sums in moving average processes with short memory and regularly varying tails. We show that the structure of the large deviation cluster in this case markedly differs from the corresponding structure in the case of exponentially light tails, considered in Chakrabarty and Samorodnitsky (2024). This is due to the difference between the “conspiracy” vs. the “catastrophe” principles underlying the large deviation events in the light tailed case and the heavy tailed case, correspondingly.
{"title":"Clustering of large deviations events in heavy-tailed moving average processes: The catastrophe principle in the short-memory case","authors":"Jiaqi Wang, Gennady Samorodnitsky","doi":"10.1016/j.spa.2025.104850","DOIUrl":"10.1016/j.spa.2025.104850","url":null,"abstract":"<div><div>How do large deviation events in a stationary process cluster? The answer depends not only on the type of large deviations, but also on the length of memory in the process. Somewhat unexpectedly, it may also depend on the tails of the process. In this paper we work in the context of large deviations for partial sums in moving average processes with short memory and regularly varying tails. We show that the structure of the large deviation cluster in this case markedly differs from the corresponding structure in the case of exponentially light tails, considered in Chakrabarty and Samorodnitsky (2024). This is due to the difference between the “conspiracy” vs. the “catastrophe” principles underlying the large deviation events in the light tailed case and the heavy tailed case, correspondingly.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"193 ","pages":"Article 104850"},"PeriodicalIF":1.2,"publicationDate":"2025-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-11DOI: 10.1016/j.spa.2025.104847
Benjamin Gess , Zhengyan Wu , Rangrang Zhang
Higher order fluctuation expansions for stochastic heat equations (SHE) with nonlinear, non-conservative and conservative noise are obtained. These Edgeworth-type expansions describe the asymptotic behavior of solutions in suitable joint scaling regimes of small noise intensity (ε → 0) and diverging singularity (δ → 0). The results include both the case of the SHE with regular and irregular diffusion coefficients. In particular, this includes the correlated Dawson-Watanabe and Dean-Kawasaki SPDEs, as well as SPDEs corresponding to the Fleming-Viot and symmetric simple exclusion processes.
{"title":"Higher order fluctuation expansions for nonlinear stochastic heat equations in singular limits","authors":"Benjamin Gess , Zhengyan Wu , Rangrang Zhang","doi":"10.1016/j.spa.2025.104847","DOIUrl":"10.1016/j.spa.2025.104847","url":null,"abstract":"<div><div>Higher order fluctuation expansions for stochastic heat equations (SHE) with nonlinear, non-conservative and conservative noise are obtained. These Edgeworth-type expansions describe the asymptotic behavior of solutions in suitable joint scaling regimes of small noise intensity (ε → 0) and diverging singularity (<em>δ</em> → 0). The results include both the case of the SHE with regular and irregular diffusion coefficients. In particular, this includes the correlated Dawson-Watanabe and Dean-Kawasaki SPDEs, as well as SPDEs corresponding to the Fleming-Viot and symmetric simple exclusion processes.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"193 ","pages":"Article 104847"},"PeriodicalIF":1.2,"publicationDate":"2025-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-11DOI: 10.1016/j.spa.2025.104848
Christian Bender , Nguyen Tran Thuan
We present a random measure approach for modeling exploration, i.e., the execution of measure-valued controls, in continuous-time reinforcement learning with controlled diffusion and jumps. We begin with the case when sampling the randomized control in continuous time takes place on a discrete-time grid and reformulate the resulting SDE as an equation driven by suitable random measures. Our main result is a limit theorem for these random measures as the mesh-size of the sampling grid goes to zero. The resulting limit SDE can be applied for the theoretical analysis of exploratory control problems and for the derivation of learning algorithms.
{"title":"Continuous time reinforcement learning: A random measure approach","authors":"Christian Bender , Nguyen Tran Thuan","doi":"10.1016/j.spa.2025.104848","DOIUrl":"10.1016/j.spa.2025.104848","url":null,"abstract":"<div><div>We present a random measure approach for modeling exploration, i.e., the execution of measure-valued controls, in continuous-time reinforcement learning with controlled diffusion and jumps. We begin with the case when sampling the randomized control in continuous time takes place on a discrete-time grid and reformulate the resulting SDE as an equation driven by suitable random measures. Our main result is a limit theorem for these random measures as the mesh-size of the sampling grid goes to zero. The resulting limit SDE can be applied for the theoretical analysis of exploratory control problems and for the derivation of learning algorithms.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"194 ","pages":"Article 104848"},"PeriodicalIF":1.2,"publicationDate":"2025-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145814322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-11DOI: 10.1016/j.spa.2025.104849
Armand Bernou , Mitia Duerinckx , Matthieu Ménard
We consider a system of N Brownian particles, with or without inertia, interacting in the mean-field regime via a weak, smooth, long-range potential, and starting initially from an arbitrary exchangeable N-particle distribution. In this model framework, we establish a fine version of the so-called creation-of-chaos phenomenon: in weak norms, the mean-field approximation for a typical particle is shown to hold with an accuracy up to an error due solely to initial pair correlations, which is damped exponentially over time. Corresponding higher-order results are also derived in the form of higher-order correlation estimates. The approach is new and easily adaptable: we start from suboptimal correlation estimates obtained from an elementary use of Itô’s calculus on moments of the empirical measure, together with ergodic properties of the mean-field dynamics, and these bounds are then made optimal after combination with PDE estimates on the BBGKY hierarchy.
{"title":"Creation of chaos for interacting Brownian particles","authors":"Armand Bernou , Mitia Duerinckx , Matthieu Ménard","doi":"10.1016/j.spa.2025.104849","DOIUrl":"10.1016/j.spa.2025.104849","url":null,"abstract":"<div><div>We consider a system of <em>N</em> Brownian particles, with or without inertia, interacting in the mean-field regime via a weak, smooth, long-range potential, and starting initially from an arbitrary exchangeable <em>N</em>-particle distribution. In this model framework, we establish a fine version of the so-called creation-of-chaos phenomenon: in weak norms, the mean-field approximation for a typical particle is shown to hold with an accuracy <span><math><mrow><mi>O</mi><mo>(</mo><msup><mi>N</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></math></span> up to an error due solely to initial pair correlations, which is damped exponentially over time. Corresponding higher-order results are also derived in the form of higher-order correlation estimates. The approach is new and easily adaptable: we start from suboptimal correlation estimates obtained from an elementary use of Itô’s calculus on moments of the empirical measure, together with ergodic properties of the mean-field dynamics, and these bounds are then made optimal after combination with PDE estimates on the BBGKY hierarchy.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"193 ","pages":"Article 104849"},"PeriodicalIF":1.2,"publicationDate":"2025-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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