Related papers: Polynomial McKean-Vlasov SDEs
As the limit equations of mean-field particle systems perturbed by common environmental noise, the McKean-Vlasov stochastic differential equations with common noise have received a lot of attention. Moreover, past dependence is an…
We consider various approximation properties for systems driven by a Mc Kean-Vlasov stochastic differential equations (MVSDEs) with continuous coefficients, for which pathwise uniqueness holds. We prove that the solution of such equations…
Based on a class of moderately interacting particle systems, we establish a quantitative approximation for density-dependent McKean-Vlasov SDEs and the corresponding nonlinear, nonlocal PDEs. The SDE is driven by both Brownian motion and…
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…
In this paper we study the problem of semiparametric estimation for a class of McKean-Vlasov stochastic differential equations. Our aim is to estimate the drift coefficient of a MV-SDE based on observations of the corresponding particle…
We study the ergodic behaviour of the McKean-Vlasov equations driven by common, divergence-free transport noise. In particular, we show that in dimension $d\geq 2$, if the noise is mixing and sufficiently strong it can enforce the…
In this paper, we first establish the existence and uniqueness of strong solutions for multivalued McKean-Vlasov stochastic differential equations (MMVSDEs) driven by L\'evy noise with non-Lipschitz coefficients. It is important to note…
In this article we present a way of treating stochastic partial differential equations with multiplicative noise by rewriting them as stochastically perturbed evolutionary equations in the sense of \cite{picardbook}, where a general…
We study stochastic differential equations (SDEs) whose drift and diffusion coefficients are path-dependent and controlled. We construct a value process on the canonical path space, considered simultaneously under a family of singular…
In this note, under a weak monotonicity and a weak coercivity, we address strong well-posedness of McKean-Vlasov stochastic differential equations (SDEs) driven by L\'{e}vy jump processes, where the coefficients are Lipschitz continuous…
The combination of Monte Carlo methods and deep learning has recently led to efficient algorithms for solving partial differential equations (PDEs) in high dimensions. Related learning problems are often stated as variational formulations…
We present a novel numerical method for solving McKean-Vlasov forward-backward stochastic differential equations (MV-FBSDEs) with common noise, combining Picard iterations, elicitability and deep learning. The key innovation involves…
We prove the well-posedness of some non-linear stochastic differential equations in the sense of McKean-Vlasov driven by non-degenerate symmetric $\alpha$-stable L\'evy processes with values in $R^d$ under some mild H{\"o}lder regularity…
Dynamical systems that are subject to continuous uncertain fluctuations can be modelled using Stochastic Differential Equations (SDEs). Controlling such system results in solving path constrained SDEs. Broadly, these problems fall under the…
In this paper we explore the merit of relative entropy in proving weak well-posedness of McKean-Vlasov SDEs and SPDEs, extending the technique introduced in Lacker arxiv:2105.02983. In the SDE setting, we prove weak existence and uniqueness…
It is known that the transition probabilities of a solution to a classical It\^o stochastic differential equation (SDE) satisfy in the weak sense the associated Kolmogorov equation. The Kolmogorov equation is a partial differential equation…
In this paper, we introduce and study McKean-Vlasov processes of bridge type. Specifically, we examine a stochastic differential equation (SDE) of the form: $$\mathrm{d} \xi_t=-\mu(t,\mathbb{E}[\varphi_1(\xi_t)]) \frac{\xi_t}{T-t}…
The Bismut formula is a crucial tool characterizing regularities of stochastic systems, and has been extensively studied for various models. However it is not yet available for SDEs with distribution dependent noise. In this paper, we first…
We prove the well-posedness of solutions to McKean-Vlasov stochastic differential equations driven by L\'evy noise under mild assumptions where, in particular, the L\'evy measure is not required to be finite. The drift, diffusion and jump…
Via constructing an asymptotic coupling by reflection, in this paper we establish uniform-in-time estimates on probability distances for mean-field type SDEs, where the drift terms under consideration are dissipative merely in the long…