A Method to Calculate the Exit Time in Stochastic Simulations
A novel method is presented to compute the exit time for the stochastic simulation algorithm. The method is based on the addition of a series of random variables and is derived using the convolution theorem. The final distribution is derived and approximated in the frequency domain. The distribution for the final time is transformed back to the real domain and can be sampled from in a simulation. The result is an approximation of the classical stochastic simulation algorithm that requires fewer random variates. An analysis of the error and speedup compared to the stochastic simulation algorithm is presented.
FIG. 1: Schematic of the derivation. The numbers denote the steps. The derivation consists of using the convolution theorem for the addition of random variables, transforming to the frequency domain, making an approximation, then transforming back as to obtain a modifieded and smaller set of random variables.