Wm,p-solution (p⩾2) of linear degenerate backward stochastic partial differential equations in the whole space

Accelerated Finite Difference Schemes for Linear Stochastic Partial Differential Equations in the Whole Space

Forward-Backward Doubly Stochastic Differential Equations with Random Jumps and Stochastic Partial Differential-Integral Equations

In this paper, we study forward-backward doubly stochastic differential equations driven by Brownian motions and Poisson process (FBDSDEP in short). Both the probabilistic interpretation for the solutions to a class of quasilinear stochastic partial differential-integral equations (SPDIEs in short) and stochastic Hamiltonian systems arising in stochastic optimal control problems with random jum...

Application of the block backward differential formula for numerical solution of Volterra integro-differential equations

In this paper, we consider an implicit block backward differentiation formula (BBDF) for solving Volterra Integro-Differential Equations (VIDEs). The approach given in this paper leads to numerical methods for solving VIDEs which avoid the need for special starting procedures. Convergence order and linear stability properties of the methods are analyzed. Also, methods with extensive stability r...

On quasi-linear stochastic partial differential equations

We prove existence and uniqueness of the solution of a parabolic SPDE in one space dimension driven by space-time white noise, in the case of a measurable drift and a constant diffusion coefficient, as well as a comparison theorem.

Prevalence of Backward Stochastic Differential Equations with Unique Solution

Let (Wt)0≤t≤1 be an r-dimensional Wiener process defined on a probability space (Ω, , P) and let ( t)0≤t≤1 denote the natural filtration of (Wt) such that 0 contains all P-null sets of . Let ξ be an 1-measurable d-dimensional square-integrable random variable. Let f be an Rd-valued process defined on R+ ×Ω×Rd ×Rd×r with values in Rd such that for all (y,z) ∈ Rd ×Rd×r , the map (t,ω) → f (t,ω, y...