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In this paper the computational aspects of probability calculations fordynamical partial sum expressions are discussed. Such dynamical partial sumexpressions have many important applications, and examples are provided in thefields of reliability, product quality assessment, and stochastic control.While these probability calculations are ostensibly of a high dimension, andconsequently intractable in general, it is shown how a recursive integrationmethodology can be implemented to obtain exact calculations as a series oftwo-dimensional calculations. The computational aspects of the implementaion ofthis methodology, with the adoption of Fast Fourier Transforms, are discussed.

Efficient Computation of the Stochastic Behavior of Partial Sum Processes