Numerical simulations and modeling for stochastic biological systems with jumps

•We provide a new approach of simulating systems with jumps.•We give the biological explanation for stochastic integration with jumps.•How to choose integrand and stationary Poisson point process are showed.•Infinitesimal method is used to simulate biological systems with jumps. This paper gives a n...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Communications in nonlinear science & numerical simulation Jg. 19; H. 5; S. 1557 - 1568
Hauptverfasser: Zou, Xiaoling, Wang, Ke
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.05.2014
Schlagworte:
Approximation
Earthquake
Exponential distribution
Infinitesimal method
Jumping noise
Lévy process
Stationary Poisson point process
Stationary Poisson point process
Exponential distribution
Earthquake
Infinitesimal method
Jumping noise
Lévy process
ISSN:1007-5704, 1878-7274
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:•We provide a new approach of simulating systems with jumps.•We give the biological explanation for stochastic integration with jumps.•How to choose integrand and stationary Poisson point process are showed.•Infinitesimal method is used to simulate biological systems with jumps. This paper gives a numerical method to simulate sample paths for stochastic differential equations (SDEs) driven by Poisson random measures. It provides us a new approach to simulate systems with jumps from a different angle. The driving Poisson random measures are assumed to be generated by stationary Poisson point processes instead of Lévy processes. Methods provided in this paper can be used to simulate SDEs with Lévy noise approximately. The simulation is divided into two parts: the part of jumping integration is based on definition without approximation while the continuous part is based on some classical approaches. Biological explanations for stochastic integrations with jumps are motivated by several numerical simulations. How to model biological systems with jumps is showed in this paper. Moreover, method of choosing integrands and stationary Poisson point processes in jumping integrations for biological models are obtained. In addition, results are illustrated through some examples and numerical simulations. For some examples, earthquake is chose as a jumping source which causes jumps on the size of biological population.
Bibliographie:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2013.09.010