Related papers: Multivalued backward stochastic differential equat…
In this paper we prove some uniqueness results for quadratic backward stochastic differential equations without any convexity assumptions on the generator. The bounded case is revisited while some new results are obtained in the unbounded…
In this paper, we first establish the reflected backward stochastic difference equations with finite state (FS-RBSDEs for short). Then we explore the Existence and Uniqueness Theorem as well as the Comparison Theorem by "one step" method.…
We construct a Hunt process that can be described as an isotropic $\alpha$-stable L\'evy process reflected from the complement of a bounded open Lipschitz set. In fact, we introduce a new analytic method for concatenating Markov processes.…
We study the existence of solutions to backward stochastic differential equations with drivers f(t,W,y,z) that are convex in z. We assume f to be Lipschitz in y and W but do not make growth assumptions with respect to z. We first show the…
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…
We consider the Cauchy problem for semilinear parabolic equation in divergence form with obstacle. We show that under natural conditions on the right-hand side of the eqution and mild conditions on the obstacle a unique continuous solution…
In this paper, we study reflected generalized backward doubly stochastic differential equations driven by Teugels martingales associated with L\'evy process (RGBDSDELs, in short) with one continuous barrier. Under uniformly Lipschitz…
In this paper we study some properties of $\psi$-Hilfer fractional integrodifferential equations. We obtain the existence and uniqueness and other properties such as continuous dependence of solution. The tools used for obtaining our result…
We consider the Cauchy problem for semilinear parabolic equation in divergence form with obstacle. We show that under natural conditions on the right-hand side of the equation and mild conditions on the obstacle the problem has a unique…
We consider a class of reflected backward doubly stochastic differential equations with time delayed generator (in short RBDSDE with time delayed generator), in this case generator at time $t$ can depend on the values of a solution in the…
In this paper we address the problem of wave dynamics in presence of concentrated nonlinearities. Given a vector field $V$ on an open subset of $\CO^n$ and a discrete set $Y\subset\RE^3$ with $n$ elements, we define a nonlinear operator…
In this paper we consider a mean-field backward stochastic differential equation (BSDE) driven by a Brownian motion and an independent Poisson random measure. Translating the splitting method introduced by Buckdahn, Li, Peng and Rainer [6]…
The combination of the It\^o formula and the Bismut-Elworthy-Li formula implies that suitable smooth solutions of semilinear Kolmogorov partial differential equations (PDEs) are also solutions to certain stochastic fixed point equations…
In this paper, we introduce a novel, data-driven approach for solving high-dimensional Bayesian inverse problems based on partial differential equations (PDEs), called Weak Neural Variational Inference (WNVI). The method complements real…
This article deals with the existence and the uniqueness of solutions to quadratic and superquadratic Markovian backward stochastic differential equations (BSDEs for short) with an unbounded terminal condition. Our results are deeply linked…
This paper develops an $\alpha$-parametrized framework for analyzing the strong convergence of the stochastic theta (ST) method for stochastic differential equations driven by time-changed L\'evy noise (TCSDEwLNs) with time-space-dependent…
To address the ill-posedness of the inverse source problem for the one-dimensional stochastic Helmholtz equations without attenuation, this study develops a novel computational framework designed to mitigate this inherent challenge at the…
In this paper, we investigate the Markovian iteration method for solving coupled forward-backward stochastic differential equations (FBSDEs) featuring a fully coupled forward drift, meaning the drift term explicitly depends on both the…
In this paper, we first prove the Hardy-Sobolev inequality for the Hessian integral by means of a descent gradient flow of certain Hessian functionals. As an application, we study the existence and regularity results of solutions to related…
This work contributes a systematic survey and complementary insights of reflecting Brownian motion and its properties. Extension of the Skorohod problem's solution to more general cases is investigated, based on which a discussion is…