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
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)
Article
Mathematics, Applied
Pierre Cardaliaguet, Panagiotis E. Souganidis
Summary: In this study, we investigate a mean field optimal control problem that arises from the optimal control of large particle systems with non-convex forcing and terminal data. We establish that the value function, which is typically Lipschitz continuous but not in the class C-1, is actually smooth in an open and dense subset of the space of times and probability measures. This result leads to a new quantitative propagation of chaos-type phenomenon for the optimal solutions of the particle system starting from this dense subset.
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS
(2023)
Article
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
Mathematics
Yuzuru Inahama
Summary: In this paper, a support theorem of Stroock-Varadhan type is proven for pinned diffusion processes. To achieve this, two powerful results from stochastic analysis are utilized. One is quasi-sure analysis for Brownian rough path, and the other is Aida-Kusuoka-Stroock's positivity theorem for the densities of weighted laws of non-degenerate Wiener functionals.
NAGOYA MATHEMATICAL JOURNAL
(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
Automation & Control Systems
Anthony Almudevar
Summary: In this paper, contractive and nonexpansive properties for adapted stochastic processes are defined, which can be used to analyze limiting properties. Nonexpansive processes generally have finite limits, while contractive processes converge to zero almost everywhere. A general method for obtaining convergence rates is proposed. These techniques are applied to various important processes, including stochastic approximation, least-squares estimation of controlled linear models, and Q-learning.
SYSTEMS & CONTROL LETTERS
(2023)
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
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
Automation & Control Systems
J. Backhoff, F. J. Silva
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
(2017)
Article
Automation & Control Systems
J. Backhoff, F. J. Silva
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
(2017)
Article
Business, Finance
Julio Backhoff Veraguas, Francisco J. Silva
MATHEMATICS AND FINANCIAL ECONOMICS
(2018)
Article
Statistics & Probability
B. Acciaio, J. Backhoff-Veraguas, A. Zalashko
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
(2020)
Article
Mathematics, Applied
J. Backhoff-Veraguas, M. Beiglboeck, G. Pammer
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
(2019)
Article
Business, Finance
Julio Backhoff-Veraguas, Ludovic Tangpi
MATHEMATICS AND FINANCIAL ECONOMICS
(2020)
Article
Statistics & Probability
Julio Backhoff Veraguas, Mathias Beiglboeck, Manu Eder, Alois Pichler
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
(2020)
Article
Statistics & Probability
Julio Backhoff-Veraguas, Daniel Lacker, Ludovic Tangpi
ANNALS OF APPLIED PROBABILITY
(2020)
Article
Business, Finance
Julio Backhoff-Veraguas, Daniel Bartl, Mathias Beiglboeck, Manu Eder
FINANCE AND STOCHASTICS
(2020)
Article
Statistics & Probability
Julio Backhoff-Veraguas, Mathias Beiglboeck, Martin Huesmann, Sigrid Kallblad
ANNALS OF PROBABILITY
(2020)
Article
Statistics & Probability
Julio Backhoff-Veraguas, Daniel Bartl, Mathias Beiglboeck, Manu Eder
PROBABILITY THEORY AND RELATED FIELDS
(2020)
Article
Business, Finance
Julio Backhoff-Veraguas, Xin Zhang
Summary: This study examines a large population dynamic game with time-evolving types, investigating the existence, uniqueness, and convergence of dynamic Cournot-Nash equilibria. It also illustrates the previous results in a toy model of optimal liquidation with price impact.
MATHEMATICS AND FINANCIAL ECONOMICS
(2023)
Article
Statistics & Probability
Julio Backhoff-Veraguas, Mathias Beiglboeck, Gudmund Pammer
ELECTRONIC COMMUNICATIONS IN PROBABILITY
(2020)
Article
Automation & Control Systems
Beatrice Acciaio, Julio Backhoff-Veraguas, Rene Carmona
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
(2019)