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math-ph2015★ 2 cited
A small delay and correlation time limit of stochastic differential delay equations with state-dependent colored noise
Scott Hottovy, Austin McDaniel, Jan Wehr
We consider a general stochastic differential delay equation (SDDE) with state-dependent colored noises and derive its limit as the time delays and the correlation times of the noi…
math-ph2014★ 99 cited
The Smoluchowski-Kramers limit of stochastic differential equations with arbitrary state-dependent friction
Scott Hottovy, Austin McDaniel, Giovanni Volpe +1
We study a class of systems of stochastic differential equations describing diffusive phenomena. The Smoluchowski-Kramers approximation is used to describe their dynamics in the sm…