An application of the theory of semi–Markov processes in simulation

Sonia Malefaki, George Iliopoulos
2007 Recent Advances in Stochastic Modeling and Data Analysis  
Importance Sampling (IS) is a well-known Monte Carlo method which is used in order to estimate expectations with respect to a target distribution π, using a sample from another distribution g and weighting properly the output. Here, we consider IS from a different point of view. By considering the weights as sojourn times until the next jump, we associate a jump process with the weighted sample. Under certain conditions, the associated jump process is an ergodic semi-Markov process with
more » ... ry distribution π. Besides its theoretical interest, the proposed point of view has also interesting applications. Working along the lines of the above approach, we are allowed to run more convenient Markov Chain Monte Carlo algorithms. This can prove to be very useful when applied in conjunction with a discretization of the state space.
doi:10.1142/9789812709691_0026 fatcat:mmcvzjj7gfdxbjemnr6cusu7e4