title: Multivariate Markov processes for stochastic systems with delays: application to the stochastic Gompertz model with delay.
abstract: Using the method of steps, we describe stochastic processes with delays in terms of Markov diffusion processes. Thus, multivariate Langevin equations and Fokker-Planck equations are derived for stochastic delay differential equations. Natural, periodic, and reflective boundary conditions are discussed. Both Ito and Stratonovich calculus are used. In particular, our Fokker-Planck approach recovers the generalized delay Fokker-Planck equation proposed by Guillouzic et al. The results obtained are applied to a model for population growth: the Gompertz model with delay and multiplicative white noise.
authors.affiliation: Institute for Theoretical Physics, University of Münster, Wilhelm-Klemm-Strasse 9, 48149 Münster, Germany.
authors.forename: T D
authors.initials: TD
authors.lastname: Frank
mesh_terms: D055592:Biophysical Phenomena; D001703:Biophysics; D008390:Markov Chains; D008954:Models, Biological; D015999:Multivariate Analysis; D011158:Population Growth; D013269:Stochastic Processes