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Related papers: On Markovian solutions to Markov Chain BSDEs

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This work focuses on a class of semi-linear functional stochastic partial differential equations with Markovian switching, in which the switching component may have finite or countably infinite states. The well-posedness of the underlying…

Probability · Mathematics 2025-09-18 Fubao Xi , Mingkun Ye , Zuozheng Zhang

We discuss a class of Backward Stochastic Differential Equations(BSDEs) with no driving martingale. When the randomness of the driver depends on a general Markov process $X$, those BSDEs are denominated Markovian BSDEs and can be associated…

Probability · Mathematics 2017-12-29 Adrien Barrasso , Francesco Russo

We consider linear n-th order stochastic differential equations on [0,1], with linear boundary conditions supported by a finite subset of [0,1]. We study some features of the solution to these problems, and especially its conditional…

Probability · Mathematics 2007-05-23 Aureli Alabert , Marco Ferrante

We define fully coupled forward-backward stochastic differential equations on spaces related to continuous time, finite state Markov Chains. Existence and uniqueness results of the fully coupled forward-backward stochastic differential…

Probability · Mathematics 2015-04-29 Shaolin Ji , Haodong Liu , Xinling Xiao

In this paper, we discuss the solvability of backward stochastic differential equations (BSDEs) with superquadratic generators. We first prove that given a superquadratic generator, there exists a bounded terminal value, such that the…

Probability · Mathematics 2009-02-20 Freddy Delbaen , Ying Hu , Xiaobo Bao

Numerical methods for computing the solutions of Markov backward stochastic differential equations (BSDEs) driven by continuous-time Markov chains (CTMCs) are explored. The main contributions of this paper are as follows: (1) we observe…

Probability · Mathematics 2023-11-27 Akihiro Kaneko

In this paper, we are interested in path-dependent stochastic differential equations (SDEs) which are controlled by Brownian motion and its delays. Within this non-Markovian context, we give a H \"ormander-type criterion for the regularity…

Probability · Mathematics 2020-09-17 Reda Chhaibi , Ibrahim Ekren

This article deals with the numerical resolution of Markovian backward stochastic differential equations (BSDEs) with drivers of quadratic growth with respect to $z$ and bounded terminal conditions. We first show some bound estimates on the…

Probability · Mathematics 2012-01-10 Adrien Richou

For the stochastic differential equation (SDE) which has piecewise continuous arguments (PCAs), is driven by multiplicative noises and its drift coefficients are dissipative, we show that the solution at integer time is a Markov chain and…

Numerical Analysis · Mathematics 2024-09-23 Chuchu Chen , Jialin Hong , Yulan Lu

We provide a probabilistic solution of a not necessarily Markovian control problem with a state constraint by means of a Backward Stochastic Differential Equation (BSDE). The novelty of our solution approach is that the BSDE possesses a…

Optimization and Control · Mathematics 2013-06-04 Stefan Ankirchner , Monique Jeanblanc , Thomas Kruse

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).…

Optimization and Control · Mathematics 2013-01-01 Coskun Cetin

We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which a linear path functional of the…

Probability · Mathematics 2013-10-17 Salvatore Federico , Peter Tankov

This paper investigates solvability of fully coupled systems of forward-backward stochastic differential equations (FBSDEs) with irregular coefficients. In particular, we assume that the coefficients of the FBSDEs are merely measurable and…

Probability · Mathematics 2020-04-02 Peng Luo , Olivier Menoukeu-Pamen , Ludovic Tangpi

In this paper, we introduce a new kind of reflected backward stochastic differential equations (RBSDEs) driven by a martingale, in a Markov chain model, but not driven by Brownian motion, and give existence and uniqueness results for the…

Probability · Mathematics 2015-05-14 Dimbinirina Ramarimbahoaka , Zhe Yang , Robert J. Elliott

In this paper, we extend the results of Elliott and Yang \cite{elliott3} and discuss the control of a stochastic process for which the driving noise is provided by a martingale associated with a semi-Markov Chain. An existence and a…

Probability · Mathematics 2025-12-23 Robert J. Elliott , Zhe Yang

We construct a Markov family of solutions for the 3D Navier-Stokes equation perturbed by a non degenerate noise. We improve the result of [DPD-NS3D] in two directions. We see that in fact not only a transition semigroup but a Markov family…

Analysis of PDEs · Mathematics 2007-05-23 Arnaud Debussche , Cyril Odasso

In the present paper, we consider multidimensional nonlinear backward stochastic differential equations (BSDEs) with a driver depending on the martingale part $M$ of a solution. We assume that the nonlinear term is merely monotone…

Probability · Mathematics 2023-08-22 Tomasz Klimsiak , Maurycy Rzymowski

The aim of this paper is to establish the existence and uniqueness of the solution to a system of nonlinear fully coupled forward-backward doubly stochastic differential equations with Poisson jumps. Our system is Markovian in the sense…

Probability · Mathematics 2018-09-19 AbdulRahman Al-Hussein , Boulakhras Gherbal

We consider an Ito stochastic differential equation with delay, driven by brownian motion, whose solution, by an appropriate reformulation, defines a Markov process $X$ with values in a space of continuous functions $\mathbf C$, with…

Probability · Mathematics 2013-04-10 Marco Fuhrman , Federica Masiero , Gianmario Tessitore

In this note, we extend some recent results on systems of backward stochastic differential equations (BSDEs) with quadratic growth to the case of coupled forward-backward stochastic differential equations (FBSDEs). We work in a Markovian…

Probability · Mathematics 2023-04-05 Joe Jackson