Related papers: Backward stochastic differential equations with ti…
The aim of the present paper is to study the regularity properties of the solution of a backward stochastic differential equation with a monotone generator in infinite dimension. We show some applications to the nonlinear Kolmogorov…
Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…
In this note, we present a new numerical method for solving backward stochastic differential equations. Our method can be viewed as an analogue of the classical finite element method solving deterministic partial differential equations.
We consider a class of stochastic control problems with a delayed control, both in drift and diffusion, of the type dX t = $\alpha$ t--d (bdt + $\sigma$dW t). We provide a new characterization of the solution in terms of a set of Riccati…
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 investigate a class of quadratic backward stochastic differential equations (BSDEs) with generators singular in $ y $. First, we establish the existence of solutions and a comparison theorem, thereby extending results in the literature.…
In backward error analysis, an approximate solution to an equation is compared to the exact solution to a nearby modified equation. In numerical ordinary differential equations, the two agree up to any power of the step size. If the…
The connection between forward backward doubly stochastic differential equations and the optimal filtering problem is established without using the Zakai's equation. The solutions of forward backward doubly stochastic differential equations…
In this paper, we introduce the notion of boundary delay equations, establishing a unified framework for analyzing linear time-invariant systems with pure time-delayed boundary conditions. We establish mild sufficient conditions for the…
The aim of this article is to study the asymptotic behaviour for large times of solutions to a certain class of stochastic partial differential equations of parabolic type. In particular, we will prove the backward uniqueness result and the…
We consider a stable driven degenerate stochastic differential equation, whose coefficients satisfy a kind of weak H{\"o}rmander condition. Under mild smoothness assumptions we prove the uniqueness of the martingale problem for the…
In this paper, we establish the existence of the solutions $ (X, L)$ of reflected stochastic differential equations with possible anticipating initial random variables. The key is to obtain some substitution formula for Stratonovich…
We introduce a novel numerical approach for a class of stochastic dynamic programs which arise as discretizations of backward stochastic differential equations or semi-linear partial differential equations. Solving such dynamic programs…
This paper is concerned with the backward stochastic differential equations whose generator is a weighted fractional Brownian field: $Y_t=\xi+\int_t^T Y_s W (ds,B_s) -\int_t^T Z_sdB_s$, $0\le t\le T$, where $W$ is a $(d+1)$-parameter…
This paper focuses on time-varying delayed stochastic differential systems with stochastically switching parameters formulated by a unified switching behavior combining a discrete adapted process and a Cox process. Unlike prior studies…
In this paper we are concerned with one-dimensional backward stochastic differential equations (BSDE in short) of the following type: \[Y_t=\xi -\int_{t\wedge \tau}^{\tau}Y_r|Y_r|^q dr-\int_{t\wedge \tau}^{\tau}Z_r dB_r,\qquad t\geq 0,\]…
In this paper, we present martingale decomposition on time scales. We establish the related backward stochastic dynamic equations on time scales (this paper BS$\nabla$E for short, concerning $\nabla$-integral on time scales) which unify…
Partial differential equations with discrete (concentrated) state-dependent delays in the space of continuous functions are investigated. In general, the corresponding initial value problem is not well posed, so we find an additional…
In this paper, we consider the solvability problems for the fully coupled forward-backward stochastic difference equations (FBS{\Delta}Es) on spaces related to discrete time, finite state processes. On one hand, we provide the necessary and…
We address our attention to the numerical time discretization of stochastic Poisson systems via Poisson integrators. The aim of the investigation regards the backward error analysis of such integrators to reveal their ability of being…