Transition rates for stochastic delay differential equations (Q2722409)

The authors consider the stochastic delay differential equation NEWLINE\[NEWLINEdX(t)=f(X(t-\tau)) dt+ \sigma dW(t),NEWLINE\]NEWLINE where \(f\) is the derivative of a double-well potential. A Fokker-Planck equation for the transition probabilities can be stated in terms of the so-called conditional average drift (CAD), cf. the authors' former paper [Small delay approximation of stochastic delay differential equations, Physical Review E 59, No. 4, 3970-3982 (1999)]. Approximating this CAD by a stationary version, the authors are able to derive an approximate steady state (invariant) density, which agrees with Monte-Carlo simulations for a quartic potential.NEWLINENEWLINEFor the entire collection see [Zbl 0958.00031].