Related papers: Stochastic functional differential equations drive…
We show a concise extension of the monotone stability approach to backward stochastic differential equations (BSDEs) that are jointly driven by a Brownian motion and a random measure for jumps, which could be of infinite activity with a…
In this paper, we prove the existence and uniqueness of the solution for neutral stochastic differential delay equations with locally monotone coefficients by using numerical approximation. An example is provided to illustrate our theory.
We establish Harnack inequality and shift Harnack inequality for stochastic differential equation driven by $G$-Brownian motion. As applications, the uniqueness of invariant linear expectations and estimates on the $\sup$-kernel are…
In this paper, we aim to develop a new weak formulation that ensures well-posedness for a broad range of stochastic partial differential equations with pseudo-differential operators whose symbols depend only on time and spatial frequencies.…
In this article we study a class of stochastic functional differential equations driven by L\'{e}vy processes (in particular, $\alpha$-stable processes), and obtain the existence and uniqueness of Markov solutions in small time intervals.…
It is well-known that a stochastic differential equation (sde) on a Euclidean space driven by a (possibly infinite-dimensional) Brownian motion with Lipschitz coefficients generates a stochastic flow of homeomorphisms. If the Lipschitz…
We study existence and uniqueness for one-dimensional generalized stochastic differential equations with singular coefficients, including distributional drift and degenerate, possibly discontinuous, diffusion coefficients. Such…
We study existence and uniqueness of solutions for second order ordinary stochastic differential equations with Dirichlet boundary conditions on a given interval. In the first part of the paper we provide sufficient conditions to ensure…
The paper is concerned with the existence and uniqueness of a strong solution to a two-dimensional backward stochastic Navier-Stokes equation with nonlinear forcing, driven by a Brownian motion. We use the spectral approximation and the…
Since the celebrated paper by El Karoui, Peng and Quenez [Mathematical Finance, 7 (1997), 1--71], backward stochastic differential equations have found wide applications in stochastic control, financial technology and machine learning. In…
We prove the existence and uniqueness of the mild solution for a nonlinear stochastic heat equation defined on an unbounded spatial domain. The nonlinearity is not assumed to be globally, or even locally, Lipschitz continuous. Instead the…
The Harnack and log Harnack inequalities for stochastic differential equation driven by $G$-Brownian motion with multiplicative noise are derived by means of coupling by change of mesure. All of the above results extend the existing ones in…
We consider one-dimensional stochastic differential equations with a boundary condition, driven by a Poisson process. We study existence and uniqueness of solutions and the absolute continuity of the law of the solution. In the case when…
In this paper, we consider a class of stochastic delay fractional evolution equations driven by fractional Brownian motion in a Hilbert space. Sufficient conditions for the existence and uniqueness of mild solutions are obtained. An…
This paper is devoted to a nonlinear singular Riemann-Liouville type fractional differential equation, the local existence of whose continuous solutions under the weakest condition remained as an open problem until now. The singularity of…
This paper addresses the challenging numerical simulation of nonlinear hybrid stochastic functional differential equations with infinite delays. We first propose an explicit scheme using space and time truncation, requiring only finite…
We prove existence and uniqueness of L^p solutions of reflected backward stochastic differential equations with p-integrable data and generators satisfying the monotonicity condition. We also show that the solution may be approximated by…
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…
We present a theory of backward stochastic differential equations in continuous time with an arbitrary filtered probability space. No assumptions are made regarding the left continuity of the filtration, of the predictable quadratic…
Determination of stability and instability of singular points in nonlinear dynamical systems is an important issue that has attracted considerable attention in different fields of engineering and science. So far, different well-defined…