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This paper studies the asymptotic behavior of the mild solution for a class of perturbed impulsive neutral stochastic functional differential equations driven by fractional Brownian motion in Hilbert space. We establish the conditions under which the mild solutions of perturbed impulsive neutral stochastic functional differential equation and the unperturbed one are close on finite time interval when the perturbation tends to zero. Moreover, we show the result holds on time interval whose length tends to infinity as the perturbation tends to zero. As an application, the asymptotic behavior of the mild solution for a class of perturbed impulsive neutral stochastic partial differential equations driven by fractional Brownian motion in Hilbert space is proposed to show the feasibility of the obtained result.

In this paper, we prove the existence and uniqueness of a solution for a class of multi-valued stochastic differential equations driven by G-Brownian motion (MSDEG) by means of the Yosida approximation method. Moreover, we set up an optimality principle of stochastic control problem and prove the value function of the control problem is the unique viscosity solution of a class of nonlinear partial differential variational inequalities.

In this paper, we deal with a class of mean-field backward stochastic differential equations in continuous time with an arbitrary filtered probability space. We prove the existence and uniqueness of a solution for those equations with strengthened Lipschitz assumption. A comparison theorem is also established.

In this paper, we establish the $p$-th moment exponential stability and quasi sure exponential stability of the solutions to impulsive stochastic differential equations driven by $G$-Brownian motion (IGSDEs in short) by means of $G$-Lyapunov function method. An example is presented to illustrate the efficiency of the obtained results.

In this paper, we prove the existence and uniqueness of a solution for a class of backward stochastic differential equations driven by G-Brownian motion with subdifferential operator by means of the Moreau–Yosida approximation method. Moreover, we give a probabilistic interpretation for the viscosity solutions of a kind of nonlinear variational inequalities. Copyright © 2017 John Wiley & Sons, Ltd.

This paper is concerned with p-moment stability of solutions to stochastic differential equations driven by G-Brownian motion (GSDEs) by means of the Lyapunov function and the Ito formula. An example is given to illustrate the effectiveness of the obtained results.

In this note, we prove the existence and uniqueness of a solution for reflected backward doubly stochastic differential equations (RBDSDEs) driven by Teugels martingales associated with a Levy process under stochastic Lipschitz condition, in which the obstacle process is right continuous with left limits (cadlag).

In this note, we prove the existence and uniqueness of the solution for a class of reflected backward stochastic differential equations (RBSDEs in short) related to the subdifferential operator of a lower semi-continuous convex function, driven by Teugels martingales associated with a Levy process. Some known results are generalized and improved.

In this note, we prove the existence and uniqueness of a solution to stochastic differential equations driven by G-Brownian motion (GSDEs, for short) under global Caratheodory conditions by means of the successive approximation.

In this paper, a new class of generalized backward doubly stochastic differential equations (GBDSDEs in short) driven by Teugels martingales associated with Levy process and the integral with respect to an adapted continuous increasing process is investigated. We obtain the existence and uniqueness of solutions to these equations. A probabilistic interpretation for solutions to a class of stochastic partial differential integral equations (PDIEs in short) with a nonlinear Neumann boundary condition is given.

In this paper, a new class of backward doubly stochastic differential equations driven by Teugels martingales associated with a Lévy process satisfying some moment condition and an independent Brownian motion is investigated. We obtain the existence and uniqueness of solutions to these equations. A probabilistic interpretation for solutions to a class of stochastic partial differential integral equations is given.

In this paper, we deal with a class of mean-field backward stochastic differential equations with subdifferential operator corresponding to a lower semi-continuous convex function. By means of Yosida approximation, the existence and uniqueness of the solution is established. As an application, we give a probability interpretation for the viscosity solutions of a class of nonlocal parabolic variational inequalities.