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On the construction of Brownian house-moving and its properties
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.Comment: 78 page