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

Abstract

The purpose of this paper is to construct a new stochastic process "Brownian house-moving," which is a Brownian bridge that stays between its starting point and its terminal point. To construct this process, statements are prepared on the weak convergence of conditioned Brownian motion, a conditioned Brownian bridge, a conditioned Brownian meander, and a conditioned three-dimensional Bessel bridge. Also studied are the sample path properties of Brownian house-moving and the decomposition formula for its distribution.

Sampling Brownian house-moving

“…This paper is organized as follows. Sections 2 and 3 review the results of [2]. In Section 2, we construct the Brownian house-moving as the one-dimensional Brownian bridge conditioned to stay between its starting point and its terminal point.…”