Comparing hitting time behaviour of Markov jump processes and their diffusion approximations

Lukasz Szpruch, D.J. Higham

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)
125 Downloads (Pure)

Abstract

Markov jump processes can provide accurate models in many applications, notably chemical and biochemical kinetics, and population dynamics. Stochastic differential equations offer a computationally efficient way to approximate these processes. It is therefore of interest to establish results that shed light on the extent to which the jump and diffusion models agree. In this work we focus on mean hitting time behavior in a thermodynamic limit. We study three simple types of reactions where analytical results can be derived, and we find that the match between mean hitting time behavior of the two models is vastly different in each case. In particular, for a degradation reaction we find that the relative discrepancy decays extremely slowly, namely, as the inverse of the logarithm of the system size. After giving some further computational results, we conclude by pointing out that studying hitting times allows the Markov jump and stochastic differential equation regimes to be compared in a manner that avoids pitfalls that may invalidate other approaches.
Original languageEnglish
Pages (from-to)605-621
Number of pages16
JournalMultiscale Modeling and Simulation: A SIAM Interdisciplinary Journal
Volume8
Issue number2
Publication statusPublished - 2010

Keywords

  • birth and death process
  • Chemical Langevin Equation
  • finite differ-ence method
  • Gillespie Algorithm
  • mean exit time
  • square root process
  • stochastic
  • differential equation
  • thermodynamic limit

Fingerprint Dive into the research topics of 'Comparing hitting time behaviour of Markov jump processes and their diffusion approximations'. Together they form a unique fingerprint.

Cite this