Using Simulation to Estimate First Passage Distribution

Article Abstract:

Consider a discrete time Markov process (x subscript n, n greater than or=to 0). For a given subset Alpha of the state space, consider the problem of using simulation to estimate the number of transitions it takes the process to enter Alpha. Using estimators based on the 'observed hazard,' we are able to improve on the usual Monte Carlo estimator. We also consider the problem of estimating the distribution of the first state in Alpha to be reached, and then extend our results to continuous time. (Reprinted by Permission of Publisher).

Management science, Estimation, Markov Process, Monte Carlo Methods, Variance Reduction

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Using simulation to estimate first passage distribution

Article Abstract:

Given a defined, discrete time Markov process within a given subset of state space, simulation methods are employed to estimate the number of transitions in the Markov process before the state space is entered. The simulation techniques employed show improvement over Monte Carlo techniques of estimation, because they consider 'observed hazards'. The estimation techniques developed using the discrete time example are then extended to application to continuous time examples.

Markov processes

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Rationality in the analysis of behavioral simulation models

Article Abstract:

Simulation models used to explain organizational behavior and to predict behavior patterns often require the analyst to leave gaps in logic in order to interpret mathematical equations in real world terms. To avoid such leaps, two forms of model analysis are developed: one based on premise description, and one that partially tests simulation models. Both of these analysis methods are applied to the behavior of a sales team with decreasing sales activity.

Models, Organizational behavior, Sales personnel, Salespeople

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