Pub Date : 2025-12-01Epub Date: 2025-08-21DOI: 10.1016/j.spa.2025.104764
Lu Yu , Arnak Dalalyan
We study the problem of sampling from a target probability density function in frameworks where parallel evaluations of the log-density gradient are feasible. Focusing on smooth and strongly log-concave densities, we revisit the parallelized randomized midpoint method and investigate its properties using recently developed techniques for analyzing its sequential version. Through these techniques, we derive upper bounds on the Wasserstein distance between sampling and target densities. These bounds quantify the substantial runtime improvements achieved through parallel processing.
{"title":"Parallelized midpoint randomization for Langevin Monte Carlo","authors":"Lu Yu , Arnak Dalalyan","doi":"10.1016/j.spa.2025.104764","DOIUrl":"10.1016/j.spa.2025.104764","url":null,"abstract":"<div><div>We study the problem of sampling from a target probability density function in frameworks where parallel evaluations of the log-density gradient are feasible. Focusing on smooth and strongly log-concave densities, we revisit the parallelized randomized midpoint method and investigate its properties using recently developed techniques for analyzing its sequential version. Through these techniques, we derive upper bounds on the Wasserstein distance between sampling and target densities. These bounds quantify the substantial runtime improvements achieved through parallel processing.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"190 ","pages":"Article 104764"},"PeriodicalIF":1.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144896748","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 : 2025-12-01Epub Date: 2025-07-14DOI: 10.1016/j.spa.2025.104724
Stanislav Minsker
We study estimators of the means of a family of random variables that admit uniform, over the class of real-valued functions, non-asymptotic error bounds under minimal moment assumptions on the underlying distribution. We show that known robust methods, such as the median-of-means and Catoni’s estimators, can often be viewed as special cases of our construction. The paper’s primary contribution lies in establishing uniform bounds for the deviations of stochastic processes defined by the proposed estimators. Furthermore, we analyze the stability of these estimators within the context of the ‘adversarial contamination’ framework. Finally, we demonstrate the applicability of our methods to the problem of robust multivariate mean estimation, showing that the resulting inequalities achieve optimal dependence on the parameters of the problem.
{"title":"Uniform bounds for robust mean estimators","authors":"Stanislav Minsker","doi":"10.1016/j.spa.2025.104724","DOIUrl":"10.1016/j.spa.2025.104724","url":null,"abstract":"<div><div>We study estimators of the means of a family of random variables <span><math><mrow><mo>{</mo><mi>f</mi><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mo>,</mo><mspace></mspace><mi>f</mi><mo>∈</mo><mi>F</mi><mo>}</mo></mrow></math></span> that admit uniform, over the class <span><math><mi>F</mi></math></span> of real-valued functions, non-asymptotic error bounds under minimal moment assumptions on the underlying distribution. We show that known robust methods, such as the median-of-means and Catoni’s estimators, can often be viewed as special cases of our construction. The paper’s primary contribution lies in establishing uniform bounds for the deviations of stochastic processes defined by the proposed estimators. Furthermore, we analyze the stability of these estimators within the context of the ‘adversarial contamination’ framework. Finally, we demonstrate the applicability of our methods to the problem of robust multivariate mean estimation, showing that the resulting inequalities achieve optimal dependence on the parameters of the problem.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"190 ","pages":"Article 104724"},"PeriodicalIF":1.1,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655315","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 : 2025-12-01Epub Date: 2025-06-07DOI: 10.1016/j.spa.2025.104709
Christophe Cuny , Michael Lin
Let be a Markov operator on a general state space with invariant probability , assumed ergodic. We study conditions which yield that for every centered a non-degenerate annealed CLT and an -normalized CLT hold.
{"title":"Global central limit theorems for Markov chains","authors":"Christophe Cuny , Michael Lin","doi":"10.1016/j.spa.2025.104709","DOIUrl":"10.1016/j.spa.2025.104709","url":null,"abstract":"<div><div>Let <span><math><mi>P</mi></math></span> be a Markov operator on a general state space <span><math><mrow><mo>(</mo><mi>S</mi><mo>,</mo><mi>Σ</mi><mo>)</mo></mrow></math></span> with invariant probability <span><math><mi>m</mi></math></span>, assumed ergodic. We study conditions which yield that for <em>every</em> centered <span><math><mrow><mn>0</mn><mo>≠</mo><mi>f</mi><mo>∈</mo><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></mrow></math></span> a non-degenerate annealed CLT and an <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-normalized CLT hold.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"190 ","pages":"Article 104709"},"PeriodicalIF":1.1,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655378","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 : 2025-12-01Epub Date: 2025-06-28DOI: 10.1016/j.spa.2025.104735
Motoya Machida
Dai Pra et al., studied two notions of monotonicity for continuous-time Markov processes on a finite partially ordered set (poset). They conjectured that monotonicity equivalence holds for a poset of W-glued diamond, and that there is no other case when it has no acyclic extension. We proved their conjecture and were able to provide a complete characterization of posets for monotonicity equivalence.
Dai Pra等，研究了有限偏序集上连续时间马尔可夫过程的单调性的两个概念。他们推测w -胶合金刚石的偏序集的单调等价性成立，并且不存在其它无环扩展的情况。我们证明了他们的猜想，并给出了单调性等价的完备的偏序集的刻画。
{"title":"A complete characterization of monotonicity equivalence for continuous-time Markov processes","authors":"Motoya Machida","doi":"10.1016/j.spa.2025.104735","DOIUrl":"10.1016/j.spa.2025.104735","url":null,"abstract":"<div><div>Dai Pra et al., studied two notions of monotonicity for continuous-time Markov processes on a finite partially ordered set (poset). They conjectured that monotonicity equivalence holds for a poset of W-glued diamond, and that there is no other case when it has no acyclic extension. We proved their conjecture and were able to provide a complete characterization of posets for monotonicity equivalence.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"190 ","pages":"Article 104735"},"PeriodicalIF":1.1,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144653071","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 : 2025-12-01Epub Date: 2025-07-19DOI: 10.1016/j.spa.2025.104748
Bo Li , Guodong Pang
We introduce an interactive Hawkes shot noise process, in which the shot noise process has a Hawkes arrival process whose intensity depends on the state of the shot noise process via the self-exciting function. Namely, the shot noise process and the Hawkes process are interactive. We prove a functional law of large numbers (FLLN) and a functional central limit theorem (FCLT) for the joint dynamics of shot noise process and the Hawkes process, and characterize the effect of the interaction between them. The FLLN limit is determined by a nonlinear function determined through an integral equation. The diffusion limit is a two-dimensional interactive stochastic differential equation driven by two independent time-changed Brownian motions. The limit of the CLT-scaled shot noise process itself can be also expressed equivalently in distribution as an Ornstein–Uhlenbeck process with time-dependent parameters, unlike being a Brownian motion in the standard case without interaction. The limit of the CLT-scaled Hawkes counting process can be expressed as a sum of two independent terms, one as a time-changed Brownian motion (just as the standard case), and the other as a (Volterra type) Gaussian process represented by an Itô integral with another time-changed Brownian motion, capturing the effect of the interaction in the self-exciting function with the state of the shot noise process. To prove the joint convergence of the co-dependent Hawkes and shot noise processes, the standard techniques for Hawkes processes using the immigration-birth representations and the associated renewal equations are no longer applicable. We develop novel techniques by constructing representations for the LLN and CLT scaled processes that resemble the limits together with the associated residual terms, and then use a localization technique together with some martingale properties to prove the residual terms converge to zero and hence the joint convergence of the scaled processes. We also consider an extension of our model, an interactive marked Hawkes shot noise process, where the intensity of the Hawkes arrivals also depends on an exogenous noise, and present the corresponding FLLN and FCLT limits.
{"title":"Scaling limits for interactive Hawkes shot noise processes","authors":"Bo Li , Guodong Pang","doi":"10.1016/j.spa.2025.104748","DOIUrl":"10.1016/j.spa.2025.104748","url":null,"abstract":"<div><div>We introduce an interactive Hawkes shot noise process, in which the shot noise process has a Hawkes arrival process whose intensity depends on the state of the shot noise process via the self-exciting function. Namely, the shot noise process and the Hawkes process are interactive. We prove a functional law of large numbers (FLLN) and a functional central limit theorem (FCLT) for the joint dynamics of shot noise process and the Hawkes process, and characterize the effect of the interaction between them. The FLLN limit is determined by a nonlinear function determined through an integral equation. The diffusion limit is a two-dimensional interactive stochastic differential equation driven by two independent time-changed Brownian motions. The limit of the CLT-scaled shot noise process itself can be also expressed equivalently in distribution as an Ornstein–Uhlenbeck process with time-dependent parameters, unlike being a Brownian motion in the standard case without interaction. The limit of the CLT-scaled Hawkes counting process can be expressed as a sum of two independent terms, one as a time-changed Brownian motion (just as the standard case), and the other as a (Volterra type) Gaussian process represented by an Itô integral with another time-changed Brownian motion, capturing the effect of the interaction in the self-exciting function with the state of the shot noise process. To prove the joint convergence of the co-dependent Hawkes and shot noise processes, the standard techniques for Hawkes processes using the immigration-birth representations and the associated renewal equations are no longer applicable. We develop novel techniques by constructing representations for the LLN and CLT scaled processes that resemble the limits together with the associated residual terms, and then use a localization technique together with some martingale properties to prove the residual terms converge to zero and hence the joint convergence of the scaled processes. We also consider an extension of our model, an interactive marked Hawkes shot noise process, where the intensity of the Hawkes arrivals also depends on an exogenous noise, and present the corresponding FLLN and FCLT limits.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"190 ","pages":"Article 104748"},"PeriodicalIF":1.1,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144696962","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 : 2025-12-01Epub Date: 2025-09-11DOI: 10.1016/j.spa.2025.104771
Jevgenijs Ivanovs , Guy Latouche , Peter Taylor
Dating from the work of Neuts in the 1980s, the field of matrix-analytic methods has been developed to analyse discrete or continuous-time Markov chains with a two-dimensional state space in which the increment of a level variable is governed by an auxiliary phase variable. More recently, matrix-analytic techniques have been applied to general Markov additive models with a finite phase space. The basic assumption underlying these developments is that the process is skip-free (in the case of QBDs or fluid queues) or that it is one-sided, that is it is jump-free in one direction.
From the Markov additive perspective, traditional matrix-analytic models can be viewed as special cases: for M/G/1 and GI/M/1-type Markov chains, increments in the level are constrained to be lattice random variables and for fluid queues, they have to be piecewise linear.
In this paper we discuss one-sided lattice and non-lattice Markov additive processes in parallel. Results that are standard in one tradition are interpreted in the other, and new perspectives emerge. In particular, using three fundamental matrices, we address hitting, two-sided exit, and creeping probabilities.
{"title":"One-sided Markov additive processes with lattice and non-lattice increments","authors":"Jevgenijs Ivanovs , Guy Latouche , Peter Taylor","doi":"10.1016/j.spa.2025.104771","DOIUrl":"10.1016/j.spa.2025.104771","url":null,"abstract":"<div><div>Dating from the work of Neuts in the 1980s, the field of matrix-analytic methods has been developed to analyse discrete or continuous-time Markov chains with a two-dimensional state space in which the increment of a <em>level</em> variable is governed by an auxiliary <em>phase</em> variable. More recently, matrix-analytic techniques have been applied to general Markov additive models with a finite phase space. The basic assumption underlying these developments is that the process is skip-free (in the case of QBDs or fluid queues) or that it is <em>one-sided</em>, that is it is jump-free in one direction.</div><div>From the Markov additive perspective, traditional matrix-analytic models can be viewed as special cases: for M/G/1 and GI/M/1-type Markov chains, increments in the level are constrained to be <em>lattice</em> random variables and for fluid queues, they have to be piecewise linear.</div><div>In this paper we discuss one-sided lattice and non-lattice Markov additive processes in parallel. Results that are standard in one tradition are interpreted in the other, and new perspectives emerge. In particular, using three fundamental matrices, we address hitting, two-sided exit, and creeping probabilities.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"190 ","pages":"Article 104771"},"PeriodicalIF":1.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145104280","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 : 2025-12-01Epub Date: 2025-07-27DOI: 10.1016/j.spa.2025.104759
Vivek S. Borkar
Two time scale stochastic approximation is analyzed when the iterates on either or both time scales do not necessarily converge.
分析了任意一个或两个时间尺度上的迭代不一定收敛时的双时间尺度随机逼近。
{"title":"Stochastic approximation with two time scales: The general case","authors":"Vivek S. Borkar","doi":"10.1016/j.spa.2025.104759","DOIUrl":"10.1016/j.spa.2025.104759","url":null,"abstract":"<div><div>Two time scale stochastic approximation is analyzed when the iterates on either or both time scales do not necessarily converge.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"190 ","pages":"Article 104759"},"PeriodicalIF":1.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144739335","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 : 2025-12-01Epub Date: 2025-07-17DOI: 10.1016/j.spa.2025.104742
V. Liang, K. Borovkov
The paper analyses the sensitivity of the finite time horizon boundary non-crossing probability of a general time-inhomogeneous, one-dimensional diffusion process to perturbations of the boundary . We prove that, for time-dependent boundaries this probability is Gâteaux differentiable in directions and Fréchet-differentiable in directions where is the Cameron–Martin space, and derive a compact representation for the derivative of . Our results allow one to approximate using boundaries that are close to and for which the computation of is feasible. We also obtain auxiliary results of independent interest in both probability theory and PDE theory.
{"title":"On time-dependent boundary crossing probabilities of diffusion processes as differentiable functionals of the boundary","authors":"V. Liang, K. Borovkov","doi":"10.1016/j.spa.2025.104742","DOIUrl":"10.1016/j.spa.2025.104742","url":null,"abstract":"<div><div>The paper analyses the sensitivity of the finite time horizon boundary non-crossing probability <span><math><mrow><mi>F</mi><mrow><mo>(</mo><mi>g</mi><mo>)</mo></mrow></mrow></math></span> of a general time-inhomogeneous, one-dimensional diffusion process to perturbations of the boundary <span><math><mi>g</mi></math></span>. We prove that, for time-dependent boundaries <span><math><mrow><mi>g</mi><mo>∈</mo><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo></mrow></math></span> this probability is Gâteaux differentiable in directions <span><math><mrow><mi>h</mi><mo>∈</mo><mi>H</mi><mo>∪</mo><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span> and Fréchet-differentiable in directions <span><math><mrow><mi>h</mi><mo>∈</mo><mi>H</mi><mo>,</mo></mrow></math></span> where <span><math><mi>H</mi></math></span> is the Cameron–Martin space, and derive a compact representation for the derivative of <span><math><mi>F</mi></math></span>. Our results allow one to approximate <span><math><mrow><mi>F</mi><mrow><mo>(</mo><mi>g</mi><mo>)</mo></mrow></mrow></math></span> using boundaries <span><math><mover><mrow><mi>g</mi></mrow><mrow><mo>̄</mo></mrow></mover></math></span> that are close to <span><math><mi>g</mi></math></span> and for which the computation of <span><math><mrow><mi>F</mi><mrow><mo>(</mo><mover><mrow><mi>g</mi></mrow><mrow><mo>̄</mo></mrow></mover><mo>)</mo></mrow></mrow></math></span> is feasible. We also obtain auxiliary results of independent interest in both probability theory and PDE theory.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"190 ","pages":"Article 104742"},"PeriodicalIF":1.1,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144665965","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 : 2025-12-01Epub Date: 2025-08-06DOI: 10.1016/j.spa.2025.104762
Daniel Cirkovic , Tiandong Wang , Daren B.H. Cline
In this paper we develop a multilayer inhomogeneous random graph model (MIRG). Layers of the MIRG may consist of both single-edge and multi-edge graphs. In the single layer case, it has been shown that the regular variation of the weight distribution underlying the inhomogeneous random graph implies the regular variation of the typical degree distribution. We extend this correspondence to the multilayer case by showing that multivariate regular variation of the weight distribution implies multivariate regular variation of the asymptotic degree distribution. Furthermore, under suitable assumptions, the extremal dependence structure present in the weight distribution will be adopted by the asymptotic degree distribution. By considering the asymptotic degree distribution, a wider class of Chung–Lu and Norros–Reittu graphs may be incorporated into the MIRG layers. Additionally, we prove consistency of the Hill estimator when applied to degrees of the MIRG that have a tail index greater than 1. Simulation results indicate that, in practice, hidden regular variation may be consistently detected from an observed MIRG. Finally, we analyze user interactions on Reddit and observe that they exhibit properties of the MIRG.
{"title":"Emergence of multivariate extremes in multilayer inhomogeneous random graphs","authors":"Daniel Cirkovic , Tiandong Wang , Daren B.H. Cline","doi":"10.1016/j.spa.2025.104762","DOIUrl":"10.1016/j.spa.2025.104762","url":null,"abstract":"<div><div>In this paper we develop a multilayer inhomogeneous random graph model (MIRG). Layers of the MIRG may consist of both single-edge and multi-edge graphs. In the single layer case, it has been shown that the regular variation of the weight distribution underlying the inhomogeneous random graph implies the regular variation of the typical degree distribution. We extend this correspondence to the multilayer case by showing that multivariate regular variation of the weight distribution implies multivariate regular variation of the asymptotic degree distribution. Furthermore, under suitable assumptions, the extremal dependence structure present in the weight distribution will be adopted by the asymptotic degree distribution. By considering the asymptotic degree distribution, a wider class of Chung–Lu and Norros–Reittu graphs may be incorporated into the MIRG layers. Additionally, we prove consistency of the Hill estimator when applied to degrees of the MIRG that have a tail index greater than 1. Simulation results indicate that, in practice, hidden regular variation may be consistently detected from an observed MIRG. Finally, we analyze user interactions on Reddit and observe that they exhibit properties of the MIRG.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"190 ","pages":"Article 104762"},"PeriodicalIF":1.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144830151","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 : 2025-12-01Epub Date: 2025-08-07DOI: 10.1016/j.spa.2025.104757
Ajay Chandra , Léonard Ferdinand
We show how the flow approach of Duch (2021), with elementary differentials as coordinates as in Chandra and Ferdinand (2024), can be used to prove well-posedness for rough stochastic differential equations driven by fractional Brownian motion with Hurst index . A novelty appearing here is that we use coordinates for the flow that are indexed by trees rather than multi-indices.
{"title":"Rough differential equations in the flow approach","authors":"Ajay Chandra , Léonard Ferdinand","doi":"10.1016/j.spa.2025.104757","DOIUrl":"10.1016/j.spa.2025.104757","url":null,"abstract":"<div><div>We show how the flow approach of Duch (2021), with elementary differentials as coordinates as in Chandra and Ferdinand (2024), can be used to prove well-posedness for rough stochastic differential equations driven by fractional Brownian motion with Hurst index <span><math><mrow><mi>H</mi><mo>></mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></math></span>. A novelty appearing here is that we use coordinates for the flow that are indexed by trees rather than multi-indices.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"190 ","pages":"Article 104757"},"PeriodicalIF":1.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144863748","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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