Related papers: Generalized backward doubly stochastic differentia…

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…

We study a backward stochastic differential equation whose terminal condition is an integrable function of a local martingale and generator has bounded growth in $z$. When the local martingale is a strict local martingale, the BSDE admits…

In this paper, we consider the backward stochastic differential equation (BSDE) with generator $f(y)|z|^2,$ where the function $f$ is defined on an open interval $D$ and locally integrable. The existence and uniqueness of bounded solutions…

In this paper we propose a numerical scheme for the class of backward doubly stochastic (BDSDEs) with possible path-dependent terminal values. We prove that our scheme converge in the strong $L^2$-sense and derive its rate of convergence.…

This paper is devoted to a general solvability of a multi-dimensional backward stochastic differential equation (BSDE) of a diagonally quadratic generator $g(t,y,z)$, by relaxing the assumptions of \citet{HuTang2016SPA} on the generator and…

This paper investigates a class of generalized mean-reflected McKean-Vlasov type backward stochastic differential equations (BSDEs). Our new framework combines a mean reflection constraint on the solution's expectation with a generalized…

In this paper, we obtain stability results for backward stochastic differential equations with jumps (BSDEs) in a very general framework. More specifically, we consider a convergent sequence of standard data, each associated to their own…

In this paper, we study a class of second order backward stochastic differential equations (2BSDEs) with quadratic growth in coefficients. We first establish solvability for such 2BSDEs and then give their applications to robust utility…

In this work, we concern with the high order numerical methods for coupled forward-backward stochastic differential equations (FBSDEs). Based on the FBSDEs theory, we derive two reference ordinary differential equations (ODEs) from the…

In this paper we establish a substitution formula for stochastic differential equation driven by generalized grey noise. We then apply this formula to investigate the absolute continuity of the solution with respect to the Lebesgue measure…

In this paper we derive exact large-buffer asymptotics for a two-class Generalized Processor Sharing (GPS) model, under the assumption that the input traffic streams generated by both classes correspond to heavy-tailed L\'evy processes.…

Using properties of backward stochastic differential equations we give new proofs of some well known results on BMO martingales and improve some estimates of BMO norms.

We study a general class of nonlinear second-order variational inequalities with interconnected bilateral obstacles, related to a multiple modes switching game. Under rather weak assumptions, using systems of penalized unilateral backward…

In the spirit of Marcus canonical stochastic differential equations, we study a similar notion of rough differential equations (RDEs), notably dropping the assumption of continuity prevalent in the rough path literature. A new metric is…

We consider various approximation properties for systems driven by a Mc Kean-Vlasov stochastic differential equations (MVSDEs) with continuous coefficients, for which pathwise uniqueness holds. We prove that the solution of such equations…

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…

Mean-field backward doubly stochastic differential equations (MF-BDSDEs, for short) are introduced and studied. The existence and uniqueness of solutions for MF-BDSDEs is established. One probabilistic interpretation for the solutions to a…

Stochastic averaging for a class of backward stochastic differential equations driven by both standard and fractional Brownian motions (SFrBSDEs in short), is investigated. An averaged SFrBSDEs for the original SFrBSDEs is proposed, and…

Recently, extracting data-driven governing laws of dynamical systems through deep learning frameworks has gained a lot of attention in various fields. Moreover, a growing amount of research work tends to transfer deterministic dynamical…

Gaussian processes (GPs) with derivatives are useful in many applications, including Bayesian optimization, implicit surface reconstruction, and terrain reconstruction. Fitting a GP to function values and derivatives at $n$ points in $d$…