Related papers: Anticipated mean-field backward stochastic differe…
Assuming that the effect of the residual interaction beyond mean-field is weak and has a short memory time, two approximate treatments of correlation in fermionic systems by means of Markovian quantum jump are presented. A simplified…
In this paper we study jump-diffusion stochastic differential equations (SDEs) with a discontinuous drift coefficient and a possibly degenerate diffusion coefficient. Such SDEs appear in applications such as optimal control problems in…
This paper is devoted to solving a real valued backward stochastic differential equation with jumps where the time horizon may be finite or infinite. Under linear growth generator, we prove existence of a minimal solution. Using a…
For a class of time-inhomogeneous SDEs with jumps, we establish criteria for the existence and uniqueness of the nonnegative solutions, and examine the extinction, the explosion together with the contractivity of the solutions, which…
In the paper, stationary measures of stochastic differential equations with jumps are considered. Under some general conditions, existence of stationary measures is proved through Markov measures and Lyapunov functions. Moreover, for two…
In this paper, we consider a stochastic differential equation driven by a fractional Brownian motion (fBm) and a Wiener process and having jumps. We prove that this equation has a unique solution and show that all its moments are finite.
We study the problem of mean-field control when the state dynamics are given by general systems of forward-backward stochastic differential equations (FBSDEs) with heterogeneous mean-field interactions. Firstly, we introduce a novel…
Moderate deviation principles for stochastic differential equations driven by a Poisson random measure (PRM) in finite and infinite dimensions are obtained. Proofs are based on a variational representation for expected values of positive…
In this paper, we define a notion of second-order backward stochastic differential equations with jumps (2BSDEJs for short), which generalizes the continuous case considered by Soner, Touzi and Zhang [Probab. Theory Related Fields 153…
We study mean-field doubly reflected BSDEs. First, using the fixed point method, we show existence and uniqueness of the solution when the data which define the BSDE are $p$-integrable with $p=1$ or $p>1$. The two cases are treated…
This paper introduces a class of backward stochastic differential equations (BSDEs), whose coefficients not only depend on the value of its solutions of the present but also the past and the future. For a sufficiently small time delay or a…
In this paper, we investigate new sufficient conditions to ensure the existence of a unique global strong solution of stochastic differential equations with jumps. By using Euler approximation and by utilising a new test function…
In a preceding article, we have studied a generalization of the problem of finding a martingale on a manifold whose terminal value is known. This article completes the results obtained in the first article by providing uniqueness and…
We extend the Yamada-Watanabe condition for pathwise uniqueness to stochastic differential equations with jumps, in the special case where small jumps are summable.
In this paper, we study the multi-dimensional mean-field backward stochastic differential equations (BSDEs, for short) with quadratic growth. Under small terminal value, the existence and uniqueness are proved for the multi-dimensional…
We study the problem of existence, uniqueness and approximation of solutions of finite dimensional Stratonovich stochastic differential equations with reflecting boundary condition driven by semimartingales with jumps. As an application we…
In this paper we show irreducibility and the strong Feller property for transition probabilities of stochastic differential equations with jumps and monotone coefficients. Thus, exponential ergodicity and the spectral gap for the…
In this paper we introduce a class of forward-backward stochastic differential equations on tensor fields of Riemannian manifolds, which are related to semi-linear parabolic partial differential equations on tensor fields. Moreover, we will…
Comparison and converse comparison theorems are important parts of the research on backward stochastic differential equations. In this paper, we obtain comparison results for one dimensional backward stochastic differential equations with…
Existence and uniqueness results of fully coupled forward stochastic differential equations without drifts and backward stochastic differential equations in a degenerate case are obtained for an arbitrarily large time duration.