Related papers: On Markovian solutions to Markov Chain BSDEs
We address a general optimal switching problem over finite horizon for a stochastic system described by a differential equation driven by Brownian motion. The main novelty is the fact that we allow for infinitely many modes (or regimes,…
In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are…
In this paper, we consider the classical spin systems on unbounded lattices given by infinite-dimensional stochastic differential equations (SDEs). We assume that the stochastic forcing acts only on one particle. The other particles are not…
We derive Markovian master equations of single and interacting harmonic systems in different scenarios, including strong internal coupling. By comparing the dynamics resulting from the corresponding Markovian master equations with exact…
We establish existence, uniqueness and regularity of solution results for a class of backward stochastic partial differential equations with singular terminal condition. The equation describes the value function of non-Markovian stochastic…
Traditional partial differential equations with constant coefficients often struggle to capture abrupt changes in real-world phenomena, leading to the development of variable coefficient PDEs and Markovian switching models. Recently,…
A backward stochastic differential equation (BSDE) is an SDE of the form $-dY_t = f(t,Y_t,Z_t)dt - Z_t^*dW_t;\ Y_T = \xi$. The subject of BSDEs has seen extensive attention since their introduction in the linear case by Bismut (1973) and in…
We consider backward stochastic differential equations (BSDE) with nonlinear generators typically of quadratic growth in the control variable. A measure solution of such a BSDE will be understood as a probability measure under which the…
This paper is concerned with a class of stochastic differential equations with Markovian switching. The Malliavin calculus is used to study the smoothness of the density of the solution under a H\"{o}rmander type condition. Furthermore, we…
This paper discusses several techniques which may be used for applying the coupling method to solutions of stochastic differential equations (SDEs). They all work in dimension $d\ge 1$, although, in $d=1$ the most natural way is to use…
We analyze dynamical systems subjected to an additive noise and their deterministic limit. In this work, we will introduce a notion by which a stochastic system has something like a Markov partition for deterministic systems. For a chosen…
We produce uniform and decaying bounds in time for derivatives of the solution to the backwards Kolmogorov equation associated to a stochastic processes governed by a time dependent dynamics. These hold under assumptions over the…
An effective approach to modeling non-Markovian quantum systems is to embed a principal (quantum) system of interest into a larger quantum system. A widely employed embedding is one that uses another quantum system, referred to as the…
In this note we review recent results on existence and uniqueness of solutions of infinite-dimensional stochastic differential equations describing interacting Brownian motions on $\R^d$.
The aim of this paper is twofold. Firstly, we derive upper and lower non-Gaussian bounds for the densities of the marginal laws of the solutions to backward stochastic differential equations (BSDEs) driven by fractional Brownian motions.…
In this paper we discuss new types of differential equations which we call anticipated backward stochastic differential equations (anticipated BSDEs). In these equations the generator includes not only the values of solutions of the present…
The key difficulty to develop efficient high-order methods for integrating stochastic differential equations lies in the calculations of the multiple stochastic integrals. This letter suggests a scheme to compute the stochastic integrals…
The large deviations analysis of solutions to stochastic differential equations and related processes is often based on approximation. The construction and justification of the approximations can be onerous, especially in the case where the…
This paper considers a non-Markov control problem arising in a financial market where asset returns depend on hidden factors. The problem is non-Markov because nonlinear filtering is required to make inference on these factors, and hence…
The present paper is devoted to the study of diagonally quadratic backward stochastic differential equation with oblique reflection. Using a penalization approach, we show the existence fo a solution by providing some delicated a priori…