演講訊息 TALKS

Abstract An important problem in the theory and application of statistical methods to many areas of science and humanities is the estimation of means of functions with respect to some well-defined target distribution. If the target distribution is a probability distribution or at least a totally finite measure, at least two methods are well known: the i.i.d. Monte Carlo and Markov chain Monte Carlo. In our work, we discuss Monte Carlo methods to statistically estimate the integrals of a class of functions with respect to some distributions that may not be finite, based on regenerative processes. To establish the asymptotically consistent estimator, it is necessary to impose appropriate moment conditions on the function with respect to the target distribution. This in turn leads to important, nontrivial questions regarding the local times of such processes. The present talk focuses on regenerative stochastic processes in continuous time such as Brownian motion.