Our aim is the development and analysis of numerical schemes for approximately solving backward diffusion-wave problem, which involves a fractional derivative in time with order $\alpha\in(1,2)$. From terminal observations at two levels, i.e., $u(T_1)$ $u(T_2)$, we simultaneously recover initial data $u(0)$ $u_t(0)$ hence solution $u(t)$ all $t > 0$. First, existence, uniqueness, Lipschitz stab...

We consider a Poisson equation in Rd for the elliptic operator corresponding to an ergodic diffusion process. Optimal regularity and smoothness with respect parameter are obtained under mild conditions on coefficients. The result is then applied establish general approximation fully coupled multitime scales stochastic differential equations only Hölder continuous Four different averaged as well...

In this paper we examine a control variate estimator for quantity that can be expressed as the expectation of functional random process, is itself solution differential equation driven by fast mean-reverting ergodic forces. The same limit diffusion process approximates original when mean-reversion time goes to zero. To get an efficient estimator, propose coupling method build and process. We sh...