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This paper is concerned with the decoupling of delayed linear forward-backward stochastic differential equations (D-FBSDEs), which is much more involved than the delay-free case due to the infinite dimension caused by the delay. A new…

Optimization and Control · Mathematics 2020-09-23 Tianfu Ma , Juanjuan Xu , Huanshui Zhang

We deal with backward stochastic differential equations with time delayed generators. In this new type of equations, a generator at time t can depend on the values of a solution in the past, weighted with a time delay function for instance…

Probability · Mathematics 2010-05-27 Łukasz Delong , Peter Imkeller

It is known that Markovian forward-backward stochastic differential equations provide nonlinear Feynman-Kac representation formulae for semilinear parabolic PDEs. We show that non-Markovian forward-backward stochastic differential equations…

Probability · Mathematics 2013-06-19 Andrea Cosso

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.…

Probability · Mathematics 2025-03-17 Wenbo Wang , Guangyan Jia

Recently, there has been a growing interest in generative models based on diffusions driven by the empirical robustness of these methods in generating high-dimensional photorealistic images and the possibility of using the vast existing…

Machine Learning · Statistics 2025-05-13 Jairon H. N. Batista , Flávio B. Gonçalves , Yuri F. Saporito , Rodrigo S. Targino

We extend the wellposedness results for second order backward stochastic differential equations introduced by Soner, Touzi and Zhang \cite{stz} to the case of a bounded terminal condition and a generator with quadratic growth in the $z$…

Probability · Mathematics 2014-04-14 Dylan Possamaï , Chao Zhou

In this paper, we present a backward deep BSDE method applied to Forward Backward Stochastic Differential Equations (FBSDE) with given terminal condition at maturity that time-steps the BSDE backwards. We present an application of this…

Computational Finance · Quantitative Finance 2020-06-16 Yajie Yu , Bernhard Hientzsch , Narayan Ganesan

In this paper, we provide an estimate for the solutions of reflected backward stochastic differential equations (RBSDEs) driven by a Markov chain, derive a continuous dependence property for their solutions with respect to the parameters of…

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

In recent works it has been demonstrated that using an appropriate rescaling, linear Boltzmann-type equations give rise to a scalar fractional diffusion equation in the limit of a small mean free path. The equilibrium distributions are…

Mathematical Physics · Physics 2014-10-01 Sabine Hittmeir , Sara Merino-Aceituno

We study a class of nonlinear BSDEs with a superlinear driver process f adapted to a filtration F and over a random time interval [[0, S]] where S is a stopping time of F. The terminal condition $\xi$ is allowed to take the value +$\infty$,…

Analysis of PDEs · Mathematics 2020-11-11 Alexandre Popier , Sharoy Samuel , Ali Sezer

We show stability and locality of the minimal supersolution of a forward backward stochastic differential equation with respect to the underlying forward process under weak assumptions on the generator. The forward process appears both in…

Probability · Mathematics 2016-06-13 Samuel Drapeau , Christoph Mainberger

In this paper, we study the backward stochastic differential equation (BSDE) with two nonlinear mean reflections, which means that the constraints are imposed on the distribution of the solution but not on its paths. Based on the backward…

Probability · Mathematics 2023-07-13 Hanwu Li

In this paper, we study the solvability of a class of multi-dimensional forward backward stochastic differential equations (FBSDEs) with oblique reflection and unbounded stopping time. Under some mild assumptions on the coefficients in such…

Probability · Mathematics 2012-07-03 Soufiane Aazizi , Imade Fakhouri

This paper discusses a new type of anticipated backward stochastic differential equation with a time-delayed generator (DABSDEs, for short) driven by fractional Brownian motion, also known as fractional BSDEs, with Hurst parameter…

Probability · Mathematics 2023-05-24 Pei Zhang , Nur Anisah Mohamed , Adriana Irawati Nur Ibrahim

We study reflected solutions of one-dimensional backward doubly stochastic differential equations (BDSDEs in short). The "reflected" keeps the solution above a given stochastic process. We get the uniqueness and existence by penalization.…

Probability · Mathematics 2009-06-08 Weiqiang Yang , Yufeng Shi , Yangling Gu

In this paper, we study reflected backward stochastic differential equation (reflected BSDE in abbreviation) with rank-based data in a Markovian framework; that is, the solution to the reflected BSDE is above a prescribed boundary process…

Probability · Mathematics 2020-07-14 Zhen-Qing Chen , Xinwei Feng

We study a constrained optimal control problem with possibly degenerate coefficients arising in models of optimal portfolio liquidation under market impact. The coefficients can be random in which case the value function is described by a…

Mathematical Finance · Quantitative Finance 2015-07-22 Ulrich Horst , Jinniao Qiu , Qi Zhang

In this paper, we are concerned with the averaging problem for a class of forward-backward stochastic differential equations with reflection driven by G-Brownian motion (reflected G-FBSDEs), which corresponds to the singular perturbation…

Probability · Mathematics 2025-03-04 Mengyao Hou

This paper is devoted to a fundamental solution of a nonlinear kinetic equation involving a porous medium or fast diffusion operator acting on velocities. Such a nonlinearity has interesting scaling properties, which result in a…

Analysis of PDEs · Mathematics 2026-03-30 Giovanni Brigati , Guillaume Carlier , Jean Dolbeault

This paper addresses the difficulty of characterizing the time-varying nature of fading channels. The current time-invariant models often fall short of capturing and tracking these dynamic characteristics. To overcome this limitation, we…

Signal Processing · Electrical Eng. & Systems 2024-02-22 Eya Ben Amar , Nadhir Ben Rached , Raul Tempone , Mohamed-Slim Alouini