Density of generalized Verhulst process and Bessel process with constant drift

Zhenyu Cui, Duy Nguyen

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

In this paper, we derive exact closed-form density functions of the generalized Verhulst process and the Bessel process with constant drift, which have applications in mathematical biology and queueing theory. We propose a generic probabilistic method for deriving exact closed-form density functions for these two diffusion processes based on a novel application of the exponential measure change in [T. Hurd and A. Kuznetsov, Explicit formulas for Laplace transforms of stochastic integrals, Markov Process. Relat. Fields, 14(2):277–290, 2008], together with formulae in [A. Borodin and P. Salminen, Handbook of Brownian Motion – Facts and Formulae, Birkhäuser, Basel, 2015]. Our study generalizes several known results in the literature.

Original languageEnglish
Pages (from-to)463-473
Number of pages11
JournalLithuanian Mathematical Journal
Volume56
Issue number4
DOIs
StatePublished - 1 Oct 2016

Keywords

  • Bessel process with constant drift
  • Verhulst process
  • exponential change of measure
  • geometric Brownian motion

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