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Statistics & Probability
Nikolaos Kolliopoulos, Martin Larsson, Zeyu Zhang
Summary: This paper studies the asymptotic behavior of the normalized maxima of real-valued diffusive particles with mean-field drift interaction. The main result establishes propagation of chaos, where the normalized maxima behave as those in an i.i.d. system with each particle following the associated McKean-Vlasov limiting dynamics in the large population limit. The proof relies on a change of measure argument dependent on a delicate combinatorial analysis of the iterated stochastic integrals in the chaos expansion of the Radon-Nikodym density.
PROBABILITY THEORY AND RELATED FIELDS
(2023)
Article
Statistics & Probability
Daniel Lacker, Luc Le Flem
Summary: We prove the optimal rate of quantitative propagation of chaos, uniformly in time, for interacting diffusions. Our main examples are interactions governed by convex potentials and models on the torus with small interactions. We show that the distance between the k-particle marginal of the n-particle system and its limiting product measure is O((k/n)(2)), uniformly in time, with distance measured either by relative entropy, squared quadratic Wasserstein metric, or squared total variation. Our proof is based on an analysis of relative entropy through the BBGKY hierarchy, adapting prior work of the first author to the time-uniform case by means of log-Sobolev inequalities.
PROBABILITY THEORY AND RELATED FIELDS
(2023)
Article
Statistics & Probability
Paul-Eric Chaudru De Raynal, Igor Honore, Stephane Menozzi
Summary: In this paper, we establish strong uniqueness for a class of degenerate SDEs of weak Hormander type under suitable Holder regularity conditions. Our approach relies on the Zvonkin transform and a perturbation technique, which demonstrate the regularizing effects and duality properties based on parabolic PDE.
PROBABILITY THEORY AND RELATED FIELDS
(2022)
Article
Mathematics, Applied
Guanghai Song
Summary: The paper introduces a stochastic single-species model with predation effect in a polluted environment, proposing a threshold for species survival and providing conditions for stochastic persistence. Theoretical findings are supported by numerical simulations.
ADVANCES IN DIFFERENCE EQUATIONS
(2021)
Article
Mathematics, Applied
Famei Zheng, Guixin Hu
Summary: This research examines the impacts of white noise and telephone noise on a population model with Allee effects. It analyzes various asymptotic behaviors of the model, such as extermination, persistence, and invariant measure. The study also reveals the important roles white noise and telephone noise play in influencing these asymptotic behaviors of the model.
ADVANCES IN DIFFERENCE EQUATIONS
(2021)
Article
Mathematics, Applied
Huijie Qiao
Summary: This article considers a nonlinear filtering problem involving multiscale non-Gaussian signal processes and observation processes with jumps. Firstly, a homogenized approach is used to reduce the dimension of the signal system. Then, the convergence of the corresponding nonlinear filtering to the homogenized filtering is demonstrated using weak convergence techniques. Finally, an example is provided to illustrate the results.
STOCHASTIC ANALYSIS AND APPLICATIONS
(2022)
Article
Biology
German Enciso, Christine Sutterlin, Ming Tan, Frederic Y. M. Wan
Summary: Research shows that the observed delay in RB-to-EB conversion in the developmental cycle of Chlamydia trachomatis is crucial for maximizing EB production by the end of intracellular infection.
BULLETIN OF MATHEMATICAL BIOLOGY
(2021)
Article
Mathematics, Applied
Yanting Ji
Summary: This paper examines the convergence rate of the EM scheme for stochastic differential delay equations of neutral type, revealing that the convergence rate for SDDEs driven by Brownian motions is one-half, while for SDDEs driven by pure jump processes, the convergence rate is slower than one-half. Consequently, the convergence rate of general SDDEs of neutral type, dominated by pure jump processes, is slower than one-half.
JOURNAL OF INEQUALITIES AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Kehan Si, Zhen Wu
Summary: This paper investigates a controlled linear-quadratic-Gaussian large population system in Stackelberg games, analyzing the relationship between three types of agents and their impact on the leader agent. By variational analysis and contraction mapping method, the decentralized strategies for leader and follower agents are obtained, proving to satisfy the epsilon-Nash equilibrium property.
ADVANCES IN DIFFERENCE EQUATIONS
(2021)
