Related papers: A note on L\'evy-driven McKean-Vlasov SDEs under m…

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…

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…

In this paper, we aim to study the asymptotic behaviour for a class of McKean-Vlasov stochastic partial differential equations with slow and fast time-scales. Using the variational approach and classical Khasminskii time discretization, we…

We show the strong well-posedness of SDEs driven by general multiplicative L\'evy noises with Sobolev diffusion and jump coefficients and integrable drift. Moreover, we also study the strong Feller property, irreducibility as well as the…

In this paper, we are interested in conditional McKean-Vlasov jump diffusions, which are also termed as McKean-Vlasov stochastic differential equations with jump idiosyncratic noise and jump common noise. As far as conditional McKean-Vlasov…

This paper studies stabilities of stochastic differential equation (SDE) driven by time-changed L\'evy noise in both probability and moment sense. This provides more flexibility in modeling schemes in application areas including physics,…

We consider the asymptotics of the invariant measure for the process of the empirical spatial distribution of $N$ coupled Markov chains in the limit of a large number of chains. Each chain reflects the stochastic evolution of one particle.…

We develop adaptive time-stepping strategies for It\^o-type stochastic differential equations (SDEs) with jump perturbations. Our approach builds on adaptive strategies for SDEs. Adaptive methods can ensure strong convergence of nonlinear…

By using lower bound conditions of the L\'evy measure w.r.t. a nice reference measure, the coupling and strong Feller properties are investigated for the Markov semigroup associated with a class of linear SDEs driven by (non-cylindrical)…

This work concerns a type of path-dependent multivalued McKean-Vlasov stochastic differential equations. First of all, we prove the well-posedness for path-dependent multivalued stochastic differential equations under the Lipschitz…

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 prove the existence of weak solutions to McKean-Vlasov SDEs defined on a domain $D \subseteq \mathbb{R}^d$ with continuous and unbounded coefficients that satisfy Lyapunov type conditions, where the Lyapunov function may depend on…

The theory of one-dimensional stochastic differential equations driven by Brownian motion is classical and has been largely understood for several decades. For stochastic differential equations with jumps the picture is still incomplete,…

In this work, we propose a stochastic version of the Rosenzweig-MacArthur model solely driven by internal demographic noise, extending classical Lotka-Volterra-type systems focused on external noise. We give a criterion for the existence…

This article is a continuation of our first work \cite{chaudruraynal:frikha}. We here establish some new quantitative estimates for propagation of chaos of non-linear stochastic differential equations in the sense of McKean-Vlasov. We…

Building on results developed in https://doi.org/10.48550/arXiv.2404.14902, where It\^{o}-SDEs with possibly degenerate and discontinuous dispersion coefficient and measurable drift were analyzed with respect to a given (sub-)invariant…

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…

We extend Krylov and R\"{o}ckner's result \cite{KR} to the drift coefficients in critical Lebesgue space, and prove the existence and uniqueness of weak solutions for a class of SDEs. To be more precise, let $b: [0,T]\times{\mathbb…

In this paper we consider a class of {\it conditional McKean-Vlasov SDEs} (CMVSDE for short). Such an SDE can be considered as an extended version of McKean-Vlasov SDEs with common noises, as well as the general version of the so-called…

In this paper, the stability behaviors of stochastic differential equations (SDEs) driven by time-changed Brownian motions are discussed. Based on the generalized Lyapunov method and stochastic analysis, necessary conditions are provided…