相关论文: Non-Markovian Fully Coupled Forward-Backward Stoch…

Quantum trajectory techniques have been used in the theory of open systems as a starting point for numerical computations and to describe the monitoring of a quantum system in continuous time. Here we extend this technique and use it to…

The theory of one-dimensional stochastic differential equations driven by Brownian motion is classical and has been largely understood for several decades. For stochastic differential equations with jumps the picture is still incomplete,…

The solutions of SDEs with multiplicative noise are not Markovian. On a coarse-grained time scale they still are, but only in the "anti-Ito" case. This allows a simple computation of the most likely path. Any density peak moves along such a…

We present topological characterization of classical stochastic processes described by discrete-time Markov chains on lattices. We point out that point-gap topology of stochastic matrices entails two distinct physical consequences that…

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…

We construct a non-Markovian canonical dynamical map that accounts for systems correlated with the environment. The physical meaning of not completely positive maps is studied to obtain a theory of non-Markovian quantum dynamics. The…

A general approach to provide approximate parameterizations of the "small" scales by the "large" ones, is developed for stochastic partial differential equations driven by linear multiplicative noise. This is accomplished via the concept of…

We consider some certain nonlinear perturbations of the stochastic linear-quadratic optimization problems and study the connections between their solutions and the corresponding Markovian backward stochastic diferential equations (BSDEs).…

By modeling the interaction of an open quantum system with its environment through a natural generalization of the classical concept of continuous time random walk, we derive and characterize a class of non-Markovian master equations whose…

This paper establishes H\"{o}lder time regularity of solutions to coupled McKean-Vlasov forward-backward stochastic differential equations (MV-FBSDEs). This is not only of fundamental mathematical interest, but also essential for their…

In this paper, we investigate two families of fully coupled linear Forward-Backward Stochastic Differential Equations (FBSDE). Within these families, one could get the same well-posedness of FBSDEs with totally different structures. The…

We analyze multidimensional Markovian integral equations that are formulated with a time-inhomogeneous progressive Markov process that has Borel measurable transition probabilities. In the case of a path-dependent diffusion process, the…

We study a class of multi-stage stochastic programs, which incorporate modeling features from Markov decision processes (MDPs). This class includes structured MDPs with continuous action and state spaces. We extend policy graphs to include…

This paper is concerned with the stochastic Hamilton-Jacobi-Bellman equation with controlled leading coefficients, which is a type of fully nonlinear backward stochastic partial differential equation (BSPDE for short). In order to formulate…

A peculiar feature of It\^o's calculus is that it is an integral calculus that gives no explicit derivative with a systematic differentiation theory counterpart, as in elementary calculus. So, can we define a pathwise stochastic derivative…

We discuss two independent methods of solution of a master equation whose biased jump transition rates account for long jumps of L\'{e}vy-stable type and nonetheless admit a Boltzmannian (thermal) equilibrium to arise in the large time…

In this study, we analytically formulated the path integral representation of the conditional probabilities for non-Markovian kinetic processes in terms of the free energy of the thermodynamic system. We carry out analytically the…

By analogy with the theory of Backward Stochastic Differential Equations, we define Backward Stochastic Difference Equations on spaces related to discrete time, finite state processes. This paper considers these processes as constructions…

In this paper we study a class of combined regular and singular stochastic control problems that can be expressed as constrained BSDEs. In the Markovian case, this reduces to a characterization through a PDE with gradient constraint. But…

Backward stochastic differential equations (BSDEs) in the sense of Pardoux-Peng [Backward stochastic differential equations and quasilinear parabolic partial differential equations, Lecture Notes in Control and Inform. Sci., 176, 200--217,…