Publication at Faculty of Mathematics and Physics |
2010
Abstract
A map on the n-dimensional Eucleidian space is considered. Diffusion given by an n-dimensional stochastic differential equation dX=b(X)dt+ s(X)dB is constructed to stay in region K=[x:f(x) less or equal c] forever in a way that the boundary S=[x:f(x)=c] is either absorbing or reflecting.
The purpose of the paper is to provide easy to apply conditions on the coefficients b(x) and s(x) with the aim to exhibit simulations of the diffusion with the above properties.