by Felisa J. Vázquez-Abad and Yanick Champoux

Output Analysis

Basic Notions
Stochastic Processes:
- Finite Horizon
- Infinite Horizon
     - Batch Means
     - Regenerative

Cross Referencing:
- Topics Index
- SimSpiders Main Page

Finite Horizon Estimation

A finite horizon simulation consists of a simulation of a stochastic process over a fixed period of time, called a ``horizon''. The quantity of interest is often a function of the process at the end of this period. We suppose that we can produce independent trajectories of the process, thus obtaining a sequence of i.i.d. values.

THE CENTRAL LIMIT THEOREM: In order to approximate the estimation error, we use the asymptotic distribution of the sample average, as the simulation length (or number of trajectories) increases.

Graph showing the distribution of the estimator (dotted line) against the limiting normal distribution (solid line).

THE CONFIDENCE INTERVAL: We can use the CLT above to give an approximate confidence interval, using:

The coverage of the above confidence is the area below the dotted line btween the two red vertical lines as shown in the plot above. It may be a poor one (smaller than the desired confidence level) if the simulation length is not sufficiently long.

WARNING: When we have more information about the estimators, we can construct more accurate confidence intervals. In this primer we illustrate a common and rather general method that works under the indicated assumptions, but there exists a variety of altenative methods that should be used when possible.

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© Copyright 1998 Felisa J. Vázquez-Abad and Yanick Champoux. All rights reserved.