相关论文: Multidimensional Stable Driven McKean-Vlasov SDEs …

We present a novel distributionally robust framework for dynamic programming that uses kernel methods to design feedback control policies. Specifically, we leverage kernel mean embedding to map the transition probabilities governing the…

We investigate a McKean-Vlasov stochastic differential equation with an additive common noise and in which the interaction is through the conditional expectation. We show that, in the presence of an additive individual noise, existence and…

We investigate the dynamics of dissipative systems with stochastic forcing and focus in particular on mean-square stability. First we show, under a natural condition on the drift and diffusion, that the stochastic system is mean-square…

As an enhanced version of existing results on Kac's propagation of chaos, which describes the convergence of mean-field particle systems to a system of independent McKean-Vlasov particles as the number of particles tends to infinity, we…

Distributed stochastic optimization intertwines (i) stochastic gradient noise, (ii) communication compression, and (iii) adaptive/normalized updates. While each factor has been studied in isolation, their joint effect under realistic…

We show well-posedness for McKean--Vlasov equations with rough common noise and progressively measurable coefficients. Our results are valid under natural regularity assumptions on the coefficients, in agreement with the respective…

We study a fully-coupled system of conditional slow-fast McKean-Vlasov Stochastic Differential Equations that exhibit full dependence on both the slow and fast components, as well as on the conditional law of the slow component. Our aim is…

Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In this…

Complex models are often used to understand interactions and drivers of human-induced and/or natural phenomena. It is worth identifying the input variables that drive the model output(s) in a given domain and/or govern specific model…

In this paper, we aim to study the asymptotic behavior for multi-scale McKean-Vlasov stochastic dynamical systems. Firstly, we obtain a central limit type theorem, i.e, the deviation between the slow component $X^{\varepsilon}$ and the…

Dense suspensions of particles dispersed in liquids are central to industrial and geophysical processes and serve as model systems for out-of-equilibrium soft matter. At high particle concentrations, they exhibit stress-dependent rheology,…

Mean-field games with common noise provide a powerful framework for modeling the collective behavior of large populations subject to shared randomness, such as systemic risk in finance or environmental shocks in economics. These problems…

In this paper, we study the stability of solutions of stochastic McKean-Vlasov equations (SMVEs) via feedback control based on discrete-time state observation. By using a specific Lyapunov function, the $H_{\infty}$ stability, asymptotic…

Numerical and analytical methods are developed for the investigation of contact sets in electrostatic-elastic deflections modeling micro-electro mechanical systems. The model for the membrane deflection is a fourth-order semi-linear partial…

The linear dispersion relation for collisionless kinetic tearing instabilities is calculated for a Harris equilibrium. In contrast to the conventional 2D geometry, which considers only modes at the center of the current sheet, modes can…

We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the…

In this work, we present a general Milstein-type scheme for McKean-Vlasov stochastic differential equations (SDEs) driven by Brownian motion and Poisson random measure and the associated system of interacting particles where drift,…

A McKean-Vlasov stochastic differential equation subject to killing associated to a regularised non-conservative and path-dependent nonlinear parabolic partial differential equation is studied. The existence and pathwise uniqueness of a…

In this paper, we study the entrance measures of time-inhomogeneous McKean-Vlasov SDEs. The existence is obtained in great generality, where the system can be expanding globally and/or degenerate for numerous number of time intervals. When…

Recently in [M. Hairer, M. Hutzenthaler, and A. Jentzen, Ann. Probab. 43, 2 (2015), 468--527] and [A. Jentzen, T. M\"uller-Gronbach, and L. Yaroslavtseva, Commun. Math. Sci. 14, 6 (2016), 1477--1500] stochastic differential equations (SDEs)…