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This study aims to construct a stochastic process called "Brownianhouse-moving," which is a Brownian bridge conditioned to stay between twocurves. To construct this process, statements are prepared on the weakconvergence of conditioned Brownian motions, conditioned Brownian bridges, andconditioned three-dimensional Bessel bridges. Moreover, the sample pathproperties of Brownian house-moving are studied as well.

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