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In this paper, we investigate a class of mean reflected McKean-Vlasov stochastic differential equation, which extends the equation proposed by \cite{briand2020particles} by allowing the solution's distribution to not only constrain its…

Probability · Mathematics 2024-11-21 Shaopeng Hong , Sheng Xiao

Sticky diffusion models a Markovian particle experiencing reflection and temporary adhesion phenomena at the boundary. Numerous numerical schemes exist for approximating stopped or reflected stochastic differential equations (SDEs), but…

Numerical Analysis · Mathematics 2025-08-11 Akash Sharma

We establish a large deviation principle for time dependent trajectories (paths) of the empirical density of $N$ particles with long range interactions, for homogeneous systems. This result extends the classical kinetic theory that leads to…

Statistical Mechanics · Physics 2022-01-19 Ouassim Feliachi , Freddy Bouchet

We develop a new approach to study the long time behaviour of solutions to nonlinear stochastic differential equations in the sense of McKean, as well as propagation of chaos for the corresponding mean-field particle system approximations.…

Probability · Mathematics 2022-11-15 Alain Durmus , Andreas Eberle , Arnaud Guillin , Katharina Schuh

Large deviation theory offers a powerful and general statistical framework to study the asymptotic dynamical properties of rare events. The application of the formalism to concrete experimental situations is, however, often restricted by…

Statistical Mechanics · Physics 2023-09-13 Maxime Debiossac , Nikolai Kiesel , Eric Lutz

The paper studies the rate of convergence of the weak Euler approximation for solutions to SDEs driven by Levy processes, with Hoelder-continuous coefficients. It investigates the dependence of the rate on the regularity of coefficients and…

Probability · Mathematics 2013-05-14 R. Mikulevicius , C. Zhang

In this paper, by utilizing Wang's Harnack inequality with power and the Banach fixed point theorem, the weak well-posedness for McKean-Vlasov SDEs with integrable drift is investigated. In addition, using the decoupled method, some…

Probability · Mathematics 2021-10-19 Xing Huang , Shen Wang , Fen-Fen Yang

We develop a weak-form sparse identification method for interacting particle systems (IPS) with the primary goals of reducing computational complexity for large particle number $N$ and offering robustness to either intrinsic or extrinsic…

Machine Learning · Statistics 2022-07-20 Daniel A. Messenger , David M. Bortz

We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which a linear path functional of the…

Probability · Mathematics 2013-10-17 Salvatore Federico , Peter Tankov

Strong convergence rates for time-discrete numerical approximations of semilinear stochastic evolution equations (SEEs) with smooth and regular nonlinearities are well understood in the literature. Weak convergence rates for time-discrete…

Probability · Mathematics 2021-11-02 Arnulf Jentzen , Ryan Kurniawan

In this paper, we first derive Milstein schemes for an interacting particle system associated with point delay McKean-Vlasov stochastic differential equations (McKean-Vlasov SDEs), possibly with a drift term exhibiting super-linear growth…

Numerical Analysis · Mathematics 2023-06-21 Jianhai Bao , Christoph Reisinger , Panpan Ren , Wolfgang Stockinger

In this paper, using Zvonkin type transform, the large deviation principle is proved for stochastic differential equations with Dini continuous drifts, where the existed methods for large deviation principle are unavailable. The method and…

Probability · Mathematics 2018-12-31 Lingyan Cheng , Xing Huang

This note shows how to considerably strengthen the usual mode of convergence of an $n$-particle system to its McKean-Vlasov limit, often known as propagation of chaos, when the volatility coefficient is nondegenerate and involves no…

Probability · Mathematics 2018-05-14 Daniel Lacker

Large-deviations theory deals with tails of probability distributions and the rare events of random processes, for example spreading packets of particles. Mathematically, it concerns the exponential fall-of of the density of thin-tailed…

Statistical Mechanics · Physics 2017-07-04 Erez Aghion , David A. Kessler , Eli Barkai

We study a one-dimensional McKean-Vlasov stochastic differential equation (SDE) with a drift equal to a product of a distribution depending on the state of the process and a non-linear function depending pointwise on the law density of the…

Probability · Mathematics 2026-03-04 Luis Mario Chaparro Jaquez , Elena Issoglio , Jan Palczewski

This paper investigates the asymptotic behavior of path-dependent multivalued McKean-Vlasov stochastic differential equations perturbed by small noise. Specifically, we first establish a large deviation principle for such equations under…

Probability · Mathematics 2026-05-11 Ying Ma , Huijie Qiao

We study two problems. First, we consider the large deviation behavior of empirical measures of certain diffusion processes as, simultaneously, the time horizon becomes large and noise becomes vanishingly small. The law of large numbers…

Probability · Mathematics 2023-09-14 Amarjit Budhiraja , Pavlos Zoubouloglou

We consider a nonlinear SPDE approximation of the Dean-Kawasaki equation for independent particles. Our approximation satisfies the physical constraints of the particle system, i.e. its solution is a probability measure for all times…

Probability · Mathematics 2024-06-21 Ana Djurdjevac , Helena Kremp , Nicolas Perkowski

Stochastic differential equations (SDEs) are of utmost importance in various scientific and industrial areas. They are the natural description of dynamical processes whose precise equations of motion are either not known or too expensive to…

Methodology · Statistics 2017-11-08 Philipp Frank , Theo Steininger , Torsten A. Enßlin

We consider autonomous stochastic ordinary differential equations (SDEs) and weak approximations of their solutions for a general class of sufficiently smooth path-dependent functionals f. Based on tools from functional It\^o calculus, such…

Probability · Mathematics 2016-06-15 Mihály Kovács , Felix Lindner