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- W2047445963 abstract "The effect of rapid random jumps on the behavior of deterministically stable dynamics is considered. The random driving force (noise) is taken to be a state-dependent Markov jump process with either finite or infinite state space. While the jump rate is high $(O( 1/varepsilon ) )$, the jump size is assumed to be$O( 1 )$. For a particle that is deterministically confined to a potential well, the stationary joint probability density function of the state and noise variables, the probability distribution of the exit points, and the mean first passage time from the well are computed. In contrast to the case of white noise, where these quantities depend on a barrier height determined solely by the potential, here they depend on an effective barrier height determined by both the potential and the noise process. The method used here is to introduce the small parameter $varepsilon $, where $1/varepsilon $ is a measure of the rapid jump rate, and to employ singular perturbation methods to solve the forward and backward master equations, for the above-mentioned quantities." @default.
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- W2047445963 date "1989-12-01" @default.
- W2047445963 modified "2023-09-27" @default.
- W2047445963 title "First-Order Dynamics Driven by Rapid Markovian Jumps" @default.
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- W2047445963 doi "https://doi.org/10.1137/0149111" @default.
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