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In this paper, we consider the continuous dependence on initial values and parameters of solutions as well as invariant measures for McKean-Vlasov SDEs under distribution-dependent Lyapunov conditions. In contrast to the classical SDEs, the…

Dynamical Systems · Mathematics 2024-10-04 Jun Ma , Zhenxin Liu

We present a novel deep learning method for estimating time-dependent parameters in Markov processes through discrete sampling. Departing from conventional machine learning, our approach reframes parameter approximation as an optimization…

Based on the assumption of the existence and uniqueness of the invariant measure for McKean-Vlasov stochastic differential equations (MV-SDEs), a self-interacting process that depends only on the current and historical information of the…

Probability · Mathematics 2024-04-09 Cui Yuanping , Li Xiaoyue

In this work we continue to investigate well-posedness for stable driven McKean-Vlasov SDEs with distributional interaction kernel following the approach introduced in [8]. We specifically focus on the impact of the Besov smoothness of the…

Analysis of PDEs · Mathematics 2025-07-22 P. -E Chaudru de Raynal , J. -F Jabir , S Menozzi

In this paper, we study a two-species model in the form of a coupled system of nonlinear stochastic differential equations (SDEs) that arises from a variety of applications such as aggregation of biological cells and pedestrian movements.…

Analysis of PDEs · Mathematics 2018-10-03 Manh Hong Duong , Julian Tugaut

This paper develops a statistical framework for goodness-of-fit testing of volatility functions in McKean-Vlasov stochastic differential equations, which describe large systems of interacting particles with distribution-dependent dynamics.…

Methodology · Statistics 2025-10-15 Akram Heidari , Mark Podolskij

In the first part of the paper we develop the sensitivity analysis for the nonlinear McKean-Vlasov diffusions stressing precise estimates of growth of solutions and their derivatives with respect to the initial data, under rather general…

Probability · Mathematics 2017-12-06 Vassili Kolokoltsov , Marianna Troeva

In this short note, we establish Malliavin differentiability of McKean-Vlasov Stochastic Differential Equations (MV-SDEs) with drifts satisfying both a locally Lipschitz and a one-sided Lipschitz assumption, and where the diffusion…

Probability · Mathematics 2025-05-09 Goncalo dos Reis , Zac Wilde

In contrast to ordinary stochastic differential equations (SDEs), the numerical simulation of McKean-Vlasov stochastic differential equations (MV-SDEs) requires approximating the distribution law first. Based on the theory of propagation of…

Numerical Analysis · Mathematics 2025-06-12 Yuhang Zhang , Minghui Song

In this paper, we first establish well-posedness results for one-dimensional McKean-Vlasov stochastic differential equations (SDEs) and related particle systems with a measure-dependent drift coefficient that is discontinuous in the spatial…

Probability · Mathematics 2024-03-29 Gunther Leobacher , Christoph Reisinger , Wolfgang Stockinger

The work concerns a class of path-dependent McKean-Vlasov stochastic differential equations with unknown parameters. First, we prove the existence and uniqueness of these equations under non-Lipschitz conditions. Second, we construct…

Probability · Mathematics 2020-06-03 Meiqi Liu , Huijie Qiao

We consider in this work the convergence of a split-step Euler type scheme (SSM) for the numerical simulation of interacting particle Stochastic Differential Equation (SDE) systems and McKean-Vlasov Stochastic Differential Equations…

Probability · Mathematics 2023-03-28 Xingyuan Chen , Goncalo dos Reis

We propose a particle system of diffusion processes coupled through a chain-like network structure described by an infinite-dimensional, nonlinear stochastic differential equation of McKean-Vlasov type. It has both (i) a local chain…

Probability · Mathematics 2019-07-18 Nils Detering , Jean-Pierre Fouque , Tomoyuki Ichiba

We study a class of McKean--Vlasov Stochastic Differential Equations (MV-SDEs) with drifts and diffusions having super-linear growth in measure and space -- the maps have general polynomial form but also satisfy a certain monotonicity…

Probability · Mathematics 2025-02-03 Xingyuan Chen , Goncalo dos Reis , Wolfgang Stockinger

In this paper, we study well-posedness of McKean-Vlasov stochastic differential equations (SDE) whose drift depends pointwisely on marginal density and satisfies a local integrability condition in time-space variables. The drift and noise…

Probability · Mathematics 2025-11-20 Anh-Dung Le , Stéphane Villeneuve

We propose a novel approach to numerically approximate McKean-Vlasov stochastic differential equations (MV-SDE) using stochastic gradient descent (SGD) while avoiding the use of interacting particle systems (IPS) {and the associated…

Numerical Analysis · Mathematics 2026-01-22 Ankush Agarwal , Andrea Amato , Goncalo dos Reis , Stefano Pagliarani

Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified…

Computation · Statistics 2012-05-03 Umberto Picchini , Susanne Ditlevsen

In this paper, the well-posedness for one-dimensional path dependent McKean-Vlasov SDEs with $\alpha$($\alpha\geq \frac{1}{2}$)-H\"{o}lder continuous diffusion is investigated. Moreover, the associated quantitative propagation of chaos in…

Probability · Mathematics 2022-09-20 Xing Huang , Xucheng Wang

In this paper we mainly investigate the strong and weak well-posedness of a class of McKean-Vlasov stochastic (partial) differential equations. The main existence and uniqueness results state that we only need to impose some local…

Probability · Mathematics 2024-01-15 Wei Hong , Shanshan Hu , Wei Liu

Stochastic differential equations (SDEs) are popular tools to analyse time series data in many areas, such as mathematical finance, physics, and biology. They provide a mechanistic description of the phenomeon of interest, and their…

Methodology · Statistics 2021-02-01 Théo Michelot , Richard Glennie , Catriona Harris , Len Thomas