Related papers: Backward stochastic differential equations with no…
In this paper, we study the existence and uniqueness of solutions to the fully coupled nonlinear forward-backward stochastic differential equations driven by G-Brownian motion. Assuming that the diffusion coefficient $\sigma$ is uniformly…
Motivated from time-inconsistent stochastic control problems, we introduce a new type of coupled forward-backward stochastic systems, namely, flows of forward-backward stochastic differential equations. They are systems consisting of a…
We prove strong well-posedness for a class of stochastic evolution equations in Hilbert spaces H when the drift term is Holder continuous. This class includes examples of semilinear stochastic damped wave equations which describe elastic…
In this paper we investigate classical solution of a semi-linear system of backward stochastic integral partial differential equations driven by a Brownian motion and a Poisson point process. By proving an It\^{o}-Wentzell formula for jump…
We consider a class of Backward Stochastic Differential Equations with superlinear driver process $f$ adapted to a filtration supporting at least a $d$ dimensional Brownian motion and a Poisson random measure on ${\mathbb R}^m- \{0\}.$ We…
In this paper we derive a Bismut-Elworthy formula under assumptions weaker than the non degeneracy of the noise. By Bismut-Elworthy formula we mean a gradient type estimate on the transition semigroup of a stochastic differential equation…
In this paper we prove existence and uniqueness of a mild solution to the Young equation $dy(t)=Ay(t)dt+\sigma(y(t))dx(t)$, $t\in[0,T]$, $y(0)=\psi$. Here, $A$ is an unbounded operator which generates a semigroup of bounded linear operators…
Backward stochastic differential equations (BSDEs) belong nowadays to the most frequently studied equations in stochastic analysis and computational stochastics. In this paper we prove that Picard iterations of BSDEs with globally Lipschitz…
This article investigates the non-stationary reaction-diffusion-advection equation, emphasizing solutions with internal layers and the associated inverse problems. We examine a nonlinear singularly perturbed partial differential equation…
In this paper, we study a class of reflected backward stochastic differential equations (BSDEs) of mean-field type, where the mean-field interaction in terms of the distribution of the $Y$-component of the solution enters in both the driver…
We study the nonlinear stochastic time-fractional diffusion equations in the spatial domain $\mathbb{R}$, driven by multiplicative space-time white noise. The fractional index $\beta$ varies continuously from $0$ to $2$. The case $\beta=1$…
In this paper, we establish the existence and uniqueness of fully coupled forward-backward stochastic differential equations (FBSDEs in short) driven by anomalous sub-diffusions $B_{L_t}$ under suitable monotonicity conditions on the…
In this paper, we study linear backward stochastic differential equations driven by a class of centered Gaussian non-martingales, including fractional Brownian motion with Hurst parameter $H\in (0,1)\setminus \{\frac12\}$. We show that, for…
We study generalized backward stochastic differential equations (BSDEs) up to a random time horizon $\vartheta$, which is not a stopping time, under minimal assumptions regarding the properties of $\vartheta$. In contrast to existing works…
In this work we propose a new algorithm for solving high-dimensional backward stochastic differential equations (BSDEs). Based on the general theta-discretization for the time-integrands, we show how to efficiently use eXtreme Gradient…
We consider partial differential equations (PDEs) characterized by an upper barrier that depends on the solution itself and a fixed lower barrier, while accommodating a non-local driver. First, we show a Feynman-Kac representation for the…
We formulate a new class of stochastic partial differential equations (SPDEs), named high-order vector backward SPDEs (B-SPDEs) with jumps, which allow the high-order integral-partial differential operators into both drift and diffusion…
We first establish the existence of an unbounded solution to a backward stochastic differential equation (BSDE) with generator $g$ allowing a general growth in the state variable $y$ and a sub-quadratic growth in the state variable $z$,…
In this paper, we study the existence and uniqueness of solutions to quadratic Backward Stochastic Differential Equations (QBSDEs for short) with rough driver and square integrable terminal condition. The main idea consists in using both…
We first state a special type of It\^o formula involving stochastic integrals of both standard and fractional Brownian motions. Then we use Doss-Sussman transformation to establish the link between backward doubly stochastic differential…