Performance bounds for differential systems incurring abrupt random changes

Stochastic differential equations are sometimes used to model dynamic systems that are subject to sudden random changes. Introduction of Poisson processes is one method for modeling such changes. Determining correctly when these changes occur raises the question of system performance. Using models of this type, we define an appropriate error probability as our measure of performance, bound the error probability, and then show that the bound satisfies a partial differential equation of the backward Kolmogorov type.