Construction and sample path properties of diffusion house-moving between two curves

Abstract

This study aims to construct a stochastic process called ``diffusion house-moving,'' which is a diffusion bridge conditioned to stay between its starting point and its ending point. To construct this process, statements are prepared on the weak convergence of conditioned diffusion processes, and conditioned diffusion bridges. Moreover, the sample path properties of diffusion house-moving are studied as well.

arXiv comment49 pages