Approximation by time discretization of special stochastic evolution equations.
Approximation of attractors for multivalued random dynamical systems
Approximation of stochastic advection diffusion equations with stochastic alternating direction explicit methods
The numerical solutions of stochastic partial differential equations of Itô type with time white noise process, using stable stochastic explicit finite difference methods are considered in the paper. Basically, Stochastic Alternating Direction Explicit (SADE) finite difference schemes for solving stochastic time dependent advection-diffusion and diffusion equations are represented and the main properties of these stochastic numerical methods, e.g. stability, consistency and convergence are analyzed....
Approximation theorems of Wong-Zakai type for stochastic differential equations in infinite dimensions [Book]
Approximations to mild solutions of stochastic semilinear equations.
Approximations to mild solutions of stochastic semilinear equations with non-Lipschitz coefficients
In the present paper, using a Picard type method of approximation, we investigate the global existence of mild solutions for a class of Ito type stochastic differential equations whose coefficients satisfy conditions more general than the Lipschitz and linear growth ones.
Asymptotic Properties of Stochastic Semilinear Equations by the Method of Lower Measures
Asymptotic solutions of diffusion models for risk reserves.
Asymptotics of a Time-Splitting Scheme for the Random Schrödinger Equation with Long-Range Correlations
This work is concerned with the asymptotic analysis of a time-splitting scheme for the Schrödinger equation with a random potential having weak amplitude, fast oscillations in time and space, and long-range correlations. Such a problem arises for instance in the simulation of waves propagating in random media in the paraxial approximation. The high-frequency limit of the Schrödinger equation leads to different regimes depending on the distance of propagation, the oscillation pattern of the initial...
Attractors for stochastic reaction-diffusion equation with additive homogeneous noise
We study the asymptotic behaviour of solutions of a reaction-diffusion equation in the whole space driven by a spatially homogeneous Wiener process with finite spectral measure. The existence of a random attractor is established for initial data in suitable weighted -space in any dimension, which complements the result from P. W. Bates, K. Lu, and B. Wang (2013). Asymptotic compactness is obtained using elements of the method of short trajectories.
Axial shear modulus of a fiber-reinforced composite with random fiber cross-sections.