Beta approximations for bridge sampling

Abstract

We consider the problem of simulating X conditional on the value of X+Y, when X and Y are independent positive random variables. We propose approximate methods for sampling (X|X+Y) by approximating the fraction (X/z|X+ Y=z) with a beta random variable. We discuss applications to Levy processes and infinitely divisible distributions, and we report numerical tests for Poisson processes, tempered stable processes, and the Heston stochastic volatility model.