Stochastic solution of fractional Fokker–Planck equations with space–time-dependent coefficients

Low Rank Solution of Unsteady Diffusion Equations with Stochastic Coefficients

We study the solution of linear systems resulting from the discreitization of unsteady diffusion equations with stochastic coefficients. In particular, we focus on those linear systems that are obtained using the so-called stochastic Galerkin finite element method (SGFEM). These linear systems are usually very large with Kronecker product structure and, thus, solving them can be both timeand co...

Numerical Solution of Stochastic Differential Equations with Constant Diffusion Coefficients

We present Runge-Kutta methods of high accuracy for stochastic differential equations with constant diffusion coefficients. We analyze L2 convergence of these methods and present convergence proofs. For scalar equations a second-order method is derived, and for systems a method of order one-and-one-half is derived. We further consider a variance reduction technique based on Hermite expansions f...

On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Linear fractional differential equations with variable coefficients

This work is devoted to the study of solutions around an α-singular point x0 ∈ [a, b] for linear fractional differential equations of the form [Lnα(y)](x) = g(x, α), where [Lnα(y)](x) = y(nα)(x)+ n−1 ∑ k=0 ak(x)y (kα)(x) with α ∈ (0, 1]. Here n ∈ N , the real functions g(x) and ak(x) (k = 0, 1, . . . , n−1) are defined on the interval [a, b], and y(nα)(x) represents sequential fractional deriva...