Related papers: Anticipated mean-field backward stochastic differe…
We prove the existence of the unique solution of a general Backward Stochastic Differential Equation with quadratic growth driven by martingales. Some kind of comparison theorem is also proved.
For a mixed stochastic differential equation involving standard Brownian motion and an almost surely H\"older continuous process $Z$ with H\"older exponent $\gamma>1/2$, we establish a new result on its unique solvability. We also establish…
A theory of existence and uniqueness is developed for general stochastic differential mean field games with common noise. The concepts of strong and weak solutions are introduced in analogy with the theory of stochastic differential…
The purpose of this paper is to explore the necessary conditions for optimality of mean-field forward-backward delay control systems. A new estimate is proved, which is a powerfultool to deal with the optimal control problems of mean-field…
We prove averaging theorems for ordinary differential equations and retarded functional differential equations. Our assumptions are weaker than those required in the results of the existing literature. Usually, we require that the…
In the paper, a class of second-order McKean-Vlasov stochastic evolution equation driven by Poisson jumps with non-Lipschitz conditions is considered. The existence and uniqueness of the mild solution is established by means of the…
We consider a couple of integrodifferential PDEs arising from a stochastic Markovian control problem subjected to initial-terminal conditions. These equations correspond to the MFG system for a controlled jump-diffusion process. We prove…
In this work, we focus on an infinite horizon mean-field linear-quadratic stochastic control problem with jumps. Firstly, the infinite horizon linear mean-field stochastic differential equations and backward stochastic differential…
This paper investigates the ergodicity of stochastic functional differential equations with jumps under the Wasserstein distance by the generalized coupling method. Two key conditions are verified. The first is verified by establishing an…
This paper establishes an equilibrium existence result for a class of Mean Field Games involving Reflected Stochastic Differential Equations. The proof relies on the framework of relaxed controls and martingale problems.
We investigate the conditional McKean-Vlasov stochastic differential equations with jumps and Markovian regime-switching. We establish the strong wellposedness using L2-Wasser-stein distance on the Wasserstein space. Also, we establish the…
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…
In this paper we consider a mean-field backward stochastic differential equation (BSDE) driven by a Brownian motion and an independent Poisson random measure. Translating the splitting method introduced by Buckdahn, Li, Peng and Rainer [6]…
In this paper we consider two classes of backward stochastic differential equations. Firstly, under a Lipschitz-type condition on the generator of the equation, which can also be unbounded, we give sufficient conditions for the existence of…
In this paper, we study the existence and uniqueness of solution to a system of nonlinear fully coupled forward-backward doubly stochastic differential equations with Poisson jumps. Our work is established in infinite dimensional separable…
Quantum stochastic master equations of jump type are formulated in a general way and connections with quantum/classical hybrid systems and quantum filtering theory are discussed. By introducing the notion of ``typical trajectory", we show…
We study a class of stochastic evolution equations of jump type with random coefficients and its optimal control problem. There are three major ingredients. The first is to prove the existence and uniqueness of the solutions by continuous…
In this paper, we are interested in the issues on existence, uniqueness, and multiplicity of stationary distributions for McKean-Vlasov SDEs with jumps. In detail, with regarding to McKean-Vlasov SDEs driven by pure jump L\'{e}vy processes,…
In this paper, we deal with a class of multivalued backward doubly stochastic differential equations with time delayed coefficients. Based on a slight extension of the existence and uniqueness of solutions for backward doubly stochastic…
We study some systems of interacting fields whose evolution is given by some singular stochastic partial differential equations of mean field type. We provide a robust setting for their study and prove a well-posedness result and a…