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}
We establish a limit theorem for a new model of 3-dimensional random walk in an inhomogeneous lattice with random orientations. This model can be seen as a 3-dimensional version of the Matheron and de Marsily model [1]. This new model leads us naturally to the study of iterated random walk in random scenery, which is a new process that can be described as a random walk in random scenery evolving in a second random scenery. We use the french acronym PAPAPA for this process unprecedented in literature, and answer a question about its stochastic behaviour asked about twenty years ago by Stéphane Le Borgne.
{"title":"Iterated random walks in random scenery (PAPAPA)","authors":"Nadine Guillotin-Plantard , Françoise Pène , Frédérique Watbled","doi":"10.1016/j.spa.2025.104843","DOIUrl":"10.1016/j.spa.2025.104843","url":null,"abstract":"<div><div>We establish a limit theorem for a new model of 3-dimensional random walk in an inhomogeneous lattice with random orientations. This model can be seen as a 3-dimensional version of the Matheron and de Marsily model [1]. This new model leads us naturally to the study of iterated random walk in random scenery, which is a new process that can be described as a random walk in random scenery evolving in a second random scenery. We use the french acronym PAPAPA for this process unprecedented in literature, and answer a question about its stochastic behaviour asked about twenty years ago by Stéphane Le Borgne.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"193 ","pages":"Article 104843"},"PeriodicalIF":1.2,"publicationDate":"2025-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790418","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 : 2025-12-03DOI: 10.1016/j.spa.2025.104846
Liping Li, Jiangang Ying
The primary aim of this article is to investigate the domination relationship between two L2-semigroups using probabilistic methods. According to Ouhabaz’s domination criterion, the domination of semigroups can be transformed into relationships involving the corresponding Dirichlet forms. Our principal result establishes the equivalence between the domination of Dirichlet forms and the killing transformation of the associated Markov processes, which generalizes and completes the results in [1] and [2]. Based on this equivalence, we provide a representation of the dominated Dirichlet form using the bivariate Revuz measure associated with the killing transformation and further characterize the sandwiched Dirichlet form within the broader Dirichlet form framework. In particular, our findings apply to the characterization of operators sandwiched between the Dirichlet Laplacian and the Neumann Laplacian. For the local boundary case, we eliminate all technical conditions identified in the literature [3] and deliver a complete representation of all sandwiched operators governed by a Robin boundary condition determined by a specific quasi-admissible measure. Additionally, our results offer a comprehensive characterization of related operators in the non-local Robin boundary case, specifically resolving an open problem posed in the literature [4].
{"title":"On domination for (non-symmetric) dirichlet forms","authors":"Liping Li, Jiangang Ying","doi":"10.1016/j.spa.2025.104846","DOIUrl":"10.1016/j.spa.2025.104846","url":null,"abstract":"<div><div>The primary aim of this article is to investigate the domination relationship between two <em>L</em><sup>2</sup>-semigroups using probabilistic methods. According to Ouhabaz’s domination criterion, the domination of semigroups can be transformed into relationships involving the corresponding Dirichlet forms. Our principal result establishes the equivalence between the domination of Dirichlet forms and the killing transformation of the associated Markov processes, which generalizes and completes the results in [1] and [2]. Based on this equivalence, we provide a representation of the dominated Dirichlet form using the bivariate Revuz measure associated with the killing transformation and further characterize the sandwiched Dirichlet form within the broader Dirichlet form framework. In particular, our findings apply to the characterization of operators sandwiched between the Dirichlet Laplacian and the Neumann Laplacian. For the local boundary case, we eliminate all technical conditions identified in the literature [3] and deliver a complete representation of all sandwiched operators governed by a Robin boundary condition determined by a specific quasi-admissible measure. Additionally, our results offer a comprehensive characterization of related operators in the non-local Robin boundary case, specifically resolving an open problem posed in the literature [4].</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"193 ","pages":"Article 104846"},"PeriodicalIF":1.2,"publicationDate":"2025-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790417","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 : 2025-12-02DOI: 10.1016/j.spa.2025.104836
Wenping Cao , Zirong Zeng , Deng Zhang
We consider the 3D stochastic Navier-Stokes equations where the viscosity exponent can be larger than the Lions exponent 5/4. Though it is well-known that the Leray-Hopf solutions are unique in this high viscous regime, we prove that the uniqueness would fail in two scaling-supercritical regimes with respect to the Ladyžhenskaya-Prodi-Serrin criteria. The constructed solutions can be non-Leray-Hopf and very close to the Leray-Hopf solutions. Furthermore, we prove the vanishing noise limit result, which relates together the stochastic solutions and the deterministic convex integration solutions constructed by Buckmaster-Vicol [1] and the recent work [2].
{"title":"Non-Leray-Hopf solutions to 3D stochastic hyper-viscous Navier-Stokes equations: Beyond the lions exponent","authors":"Wenping Cao , Zirong Zeng , Deng Zhang","doi":"10.1016/j.spa.2025.104836","DOIUrl":"10.1016/j.spa.2025.104836","url":null,"abstract":"<div><div>We consider the 3D stochastic Navier-Stokes equations where the viscosity exponent can be larger than the Lions exponent 5/4. Though it is well-known that the Leray-Hopf solutions are unique in this high viscous regime, we prove that the uniqueness would fail in two scaling-supercritical regimes with respect to the Ladyžhenskaya-Prodi-Serrin criteria. The constructed solutions can be non-Leray-Hopf and very close to the Leray-Hopf solutions. Furthermore, we prove the vanishing noise limit result, which relates together the stochastic solutions and the deterministic convex integration solutions constructed by Buckmaster-Vicol [1] and the recent work [2].</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"193 ","pages":"Article 104836"},"PeriodicalIF":1.2,"publicationDate":"2025-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145737187","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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