Multivariate Markov processes for stochastic systems with delays: application to the stochastic Gompertz model with delay.

@article{Frank2002MultivariateMP,
  title={Multivariate Markov processes for stochastic systems with delays: application to the stochastic Gompertz model with delay.},
  author={Till D. Frank},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2002},
  volume={66 1 Pt 1},
  pages={
          011914
        }
}
  • Till D. Frank
  • Published 2002 in
    Physical review. E, Statistical, nonlinear, and…
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… CONTINUE READING

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