Simulating the maximum and its location for constrained Brownian processes

Music City Center 

We consider the problem of exact simulation from the joint distribution of the maximum and its location for several Brownian processes: the Brownian meander, restricted Brownian meander and the Brownian excursion. Such distributions have complicated probability density functions (pdfs), expressed in terms of infinite series. Thus, a direct sampling approach is not feasible. In this work we derive the joint pdf of the maximum and its location for the restricted Brownian meander process as an infinite series and devise exact sampling algorithms for all three processes above. We present a simulation study to assess the efficiency of our algorithms.

Brownian meander

Brownian excursion

maximum

exact simulation 

Section on Statistical Computing