Related papers: Regularity and Sensitivity for McKean-Vlasov Type …

The distribution-dependent stochastic differential equations (DDSDEs) describe stochastic systems whose evolution is determined by both the microcosmic site and the macrocosmic distribution of the particle. The density function associated…

We prove nonlinear modulational instability for both periodic and localized perturbations of periodic traveling waves for several dispersive PDEs, including the KDV type equations (e.g. the Whitham equation, the generalized KDV equation,…

This article investigates the existence, uniqueness, and regularity of solutions to nonlinear stochastic reaction-diffusion-advection equations (SRDAEs) with spatially homogeneous colored noises and infinitesimal generators of subordinate…

We develop a new generalized coupling approach to the study of stochastic delay equations with H\"older continuous coefficients, for which analytical PDE-based methods are not available. We prove that such equations possess unique weak…

We establish the existence of solutions to common noise McKean-Vlasov martingale problems for coefficients with low regularity. Our approach is able to handle the key challenge posed by drift coefficients that are discontinuous with respect…

We investigate the mean-field dynamics of stochastic McKean differential equations with heterogeneous particle interactions described by large network structures. To express a wide range of graphs, from dense to sparse structures, we…

In this paper we discuss Stochastic Differential-Algebraic Equations (SDAEs) and the asymptotic stability assessment for such systems via Lyapunov exponents (LEs). We focus on index-one SDAEs and their reformulation as ordinary stochastic…

Dynamical systems are essential to model various phenomena in physics, finance, economics, and are also of current interest in machine learning. A central modeling task is investigating parameter sensitivity, whether tuning atmospheric…

This paper concerns the stability of analytical and numerical solutions of nonlinear stochastic delay differential equations (SDDEs). We derive sufficient conditions for the stability, contractivity and asymptotic contractivity in mean…

We examine nonlinear Kolmogorov partial differential equations (PDEs). Here the nonlinear part of the PDE comes from its Hamiltonian where one maximizes over all possible drift and diffusion coefficients which fall within a…

In this survey, we provide an in-depth exposition of our recent results on the well-posedness theory for stochastic evolution equations, employing maximal regularity techniques. The core of our approach is an abstract notion of critical…

We consider a special class of mean field SDEs with common noise which depend on the image of the solution (i.e. the conditional distribution given noise). The strong well-posedness is derived under a monotone condition which is weaker than…

In this article, we show how the theory of rough paths can be used to provide a notion of solution to a class of nonlinear stochastic PDEs of Burgers type that exhibit too high spatial roughness for classical analytical methods to apply. In…

We introduce a novel paradigm for learning non-parametric drift and diffusion functions for stochastic differential equation (SDE). The proposed model learns to simulate path distributions that match observations with non-uniform time…

We deduce stability and pathwise uniqueness for a McKean-Vlasov equation with random coefficients and a multidimensional Brownian motion as driver. Our analysis focuses on a non-Lipschitz drift coefficient and includes moment estimates for…

The stochastic differential equation of McKean-Vlasov type is identified such that the Fokker-Planck equation associated to it is the Boltzmann equation. Hence, we call its solutions as Boltzmann processes. They describe the dynamics (in…

Complementing the analysis in [41], we investigate the well-posedness of SPDEs problems of doubly nonlinear type. These arise ubiquitously in the modelization of dissipative media and correspond to generalized balance laws between…

Inspired by [Fehrman, Gess; Invent. Math., 2023], we provide a fine analysis of the McKean-Vlasov PDE with singular interactions and drift terms of square root form. As the corresponding skeleton equation of Dean-Kawasaki equation with…

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…

In this paper, we investigate an optimal control problem for McKean-Vlasov stochastic partial differential equations, in which the coefficients depend on the law of the state process. For systems with nonconvex control sets, we establish a…