Related papers: Stochastic Delay Differential Equations with Jump …

We consider the Skorokhod problem in a time-varying interval. We prove existence and uniqueness for the solution. We also express the solution in terms of an explicit formula. Moving boundaries may generate singularities when they touch. We…

We study differential equations with a linear, path dependent drift and discrete delay in the diffusion term driven by a $\gamma$-H\"older rough path for $\gamma > \frac{1}{3}$. We prove well-posedness of these systems and establish a…

We consider ergodic backward stochastic differential equations in a discrete time setting, where noise is generated by a finite state Markov chain. We show existence and uniqueness of solutions, along with a comparison theorem. To obtain…

In this paper, we study the reflected backward stochastic differential equations driven by G-Brownian motion with two reflecting obstacles, which means that the solution lies between two prescribed processes. A new kind of approximate…

We develop a unified PDE-probabilistic framework for pointwise gradient and Hessian estimates of Markov semigroups associated with stochastic differential equations with singular and unbounded coefficients. Under mild local structural…

We study the long time behavior of the stochastic quantization equation. Extending recent results by Mourrat and Weber we first establish a strong non-linear dissipative bound that gives control of moments of solutions at all positive times…

In this article we study a class of delay differential equations with infinite delay in weighted spaces of uniformly continuous functions. We focus on the integrated semigroup formulation of the problem and so doing we provide an spectral…

In this paper we establish a comparison theorem for stochastic differential delay equations with jumps. An example is constructed to demonstrate that the comparison theorem need not hold whenever the diffusion term contains a delay function…

In this paper, we study the mean reflected stochastic differential equations driven by G-Brownian motion, where the constraint depends on the expectation of the solution rather than on its paths. Well-posedness is achieved by first…

We consider stochastic semilinear partial differential equations with Lipschitz nonlinear terms. We prove existence and uniqueness of an invariant measure and the existence of a solution for the corresponding Kolmogorov equation in the…

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…

This article addresses a new class of fractional nonlocal neutral stochastic differential system of order 1<q<2 including non-instantaneous impulses(NIIs) and state-dependent delay(SDD) with the Poisson jumps and the Wiener process in…

This paper is mainly concerned with a kind of fractional stochastic evolution equations driven by L\'evy noise in a bounded domain. We first state the well-posedness of the problem via iterative approximations and energy estimates. Then,…

In this work we prove the existence and uniqueness of the strong solution to the two-dimensional stochastic magneto-hydrodynamic system perturbed by Levy noise. The local monotonicity arguments have been ex- ploited in the proofs. The…

This paper presents and analyzes the compensated projected Euler-Maruyama method for stochastic differential equations with jumps under a global monotonicity condition. Compared with existing conditions, this condition allows the…

This paper focuses on stochastic partial differential equations (SPDEs) under two-time-scale formulation. Distinct from the work in the existing literature, the systems are driven by $\alpha$-stable processes with $\alpha \in(1,2)$. In…

The work concerns invariant measures for multivalued McKean-Vlasov stochastic differential equations. First of all, we prove the exponential ergodicity of these equations. Then for a sequence of these equations, when their coefficients…

We show the variational convergence of an irreversible Markov jump process describing a finite stochastic particle system to the solution of a countable infinite system of deterministic time-inhomogeneous quadratic differential equations…

We consider an Ito stochastic differential equation with delay, driven by brownian motion, whose solution, by an appropriate reformulation, defines a Markov process $X$ with values in a space of continuous functions $\mathbf C$, with…

In this paper, we present a general framework for solving stochastic functional differential equations in infinite dimensions in the sense of martingale solutions, which can be applied to a large class of SPDE with finite delays, e.g.…