Simplest random walk for approximating Robin boundary value problems and ergodic limits of reflected diffusions

Ergodic Control of Reflected Diffusions with Jumps

We discuss ergodicity properties of a controlled jumps diffusion process reflected from the boundary of a bounded domain. The control parameters act on the drift term and on a first order type jump density. The controlled process is generated via a Girsanov change of probability, and a long run average criterion is to be optimized. By means of the Hamilton-Jacobi-Bellman equation, an optimal st...

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation

Robin Boundary Value Problems on Arbitrary Domains

We develop a theory of generalised solutions for elliptic boundary value problems subject to Robin boundary conditions on arbitrary domains, which resembles in many ways that of the Dirichlet problem. In particular, we establish Lp-Lq-estimates which turn out to be the best possible in that framework. We also discuss consequences to the spectrum of Robin boundary value problems. Finally, we app...

L2-transforms for boundary value problems

In this article, we will show the complex inversion formula for the inversion of the L2-transform and also some applications of the L2, and Post Widder transforms for solving singular integral equation with trigonometric kernel. Finally, we obtained analytic solution for a partial differential equation with non-constant coefficients.

approximating initial-value problems with two-point boundary-value problems: bbm-equation