相关论文: Stochastic differential equations with jumps

Differential equations are used in a wide variety of disciplines, describing the complex behavior of the physical world. Analytic solutions to these equations are often difficult to solve for, limiting our current ability to solve complex…

In this paper, we are devoted to the numerical methods for mean-field stochastic differential equations with jumps (MSDEJs). First by using the mean-field It\^o formula [Sun, Yang and Zhao, Numer. Math. Theor. Meth. Appl., 10 (2017),…

In this work, we systematically investigate linear multi-step methods for differential equations with memory. In particular, we focus on the numerical stability for multi-step methods. According to this investigation, we give some…

The method of Lyapunov functions is one of the most effective ones for the investigation of stability of dynamical systems, in particular, of stochastic differential systems. The main purpose of the paper is the analysis of the stability of…

A stochastic differential equation with infinite memory is considered. The drift coefficient of the equation is a nonlinear functional of the past history of the solution. Sufficient conditions for existence and uniqueness of stationary…

Randomness is ubiquitous in modern engineering. The uncertainty is often modeled as random coefficients in the differential equations that describe the underlying physics. In this work, we describe a two-step framework for numerically…

In this paper we show the existence and uniqueness of a solution for a stochastic differential equation driven by an additive noise which is the sum of two fractional Brownian motions with different Hurst parameters. The proofs are based on…

We formulate a new class of stochastic partial differential equations (SPDEs), named high-order vector backward SPDEs (B-SPDEs) with jumps, which allow the high-order integral-partial differential operators into both drift and diffusion…

In this paper we discuss the stability of stochastic differential equations and the interplay between the moment stability of a SDE and the topology of the underlying manifold. Sufficient and necessary conditions are given for the moment…

A new notion of stochastic transformation is proposed and applied to the study of both weak and strong symmetries of stochastic differential equations (SDEs). The correspondence between an algebra of weak symmetries for a given SDE and an…

This work concerns a type of coupled McKean-Vlasov stochastic differential equations (MVSDEs in short) with jumps. First, we prove superposition principles for these coupled MVSDEs with jumps and non-local space-distribution dependent…

Stochastic partial differential equations (SPDEs) represent a very active research field with numerous recent developments and breakthrough results. There are several well-established approaches and methods used to construct solutions for…

This paper considers some the existence and uniqueness of strong solutions of stochastic neutral functional differential equations. The conditions on the neutral functional relax those commonly used to establish the existence and uniqueness…

We develop the rough path counterpart of It\^o stochastic integration and - differential equations driven by general semimartingales. This significantly enlarges the classes of (It\^o / forward) stochastic differential equations treatable…

This paper deals a continuous-time state-dependent jump linear system, a particular kind of stochastic switching system. In particular, we consider a situation when the transition rate of the random jump process depends on the state…

This paper study a type of fully coupled mean-field forward-backward stochastic differential equations with jumps under the monotonicity condition, including the existence and the uniqueness of the solution of our equation as well as the…

This manuscript is a self-contained overview of essential results of stochastic calculus and stochastic differential equations, and their connection with final-value problems for second order linear PDEs.

We study various solution behaviors of scale equations which are recently proposed in \cite{Kim}. On the contrary to conventional mathematical tools, scale equations are capable to accommodate various behaviors at different scale levels…

We consider nonlinear integro-differential equations, like the ones that arise from stochastic control problems with purely jump L\`evy processes. We obtain a nonlocal version of the ABP estimate, Harnack inequality, and interior…

We consider one-dimensional stochastic differential equations with a boundary condition, driven by a Poisson process. We study existence and uniqueness of solutions and the absolute continuity of the law of the solution. In the case when…