Abstract:In this article, we study the dynamics of a system governed by an ordinary differential equation under the combined influence of fast periodic sampling with period δ and small jump noise of size ε, 0 < ε, δ ≪ 1. The noise is a combination of Brownian motion and Poisson random measure. The instantaneous rate of change of the state depends not only on its current value but on the most recent measurement of the state, as the state is measured at certain discrete-time instants. As ε, δ ց 0, the stochastic process … Show more
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