Sampling Brownian house-moving

抄録

We numerically generate a stochastic process called ``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 bridges. We also study the sample path properties of Brownian house-moving and the decomposition formula for its distribution. Using this decomposition formula and a Monte Carlo sampling technique for a BES$(3)$-bridge, we are able to numerically generate Brownian house-moving at discrete times.