Some results on the generalized Brownian bridge

Abstract

Abstract The generalized Brownian bridge X a , b , T {X^{a,b,T}} from a to b of length T was used in several fields such as in mathematical finance, biology and statistics. In this paper, we study the following stochastic properties and characteristics of this process: The Hölder continuity, the self-similarity, the quadratic variation, the Markov property, the stationarity of the increments, and the α-differentiability of the trajectories.