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Introduction to Stochastic Models in Biology

  • Susanne Ditlevsen
  • Adeline Samson
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2058)

Abstract

This chapter is concerned with continuous time processes, which are often modeled as a system of ordinary differential equations (ODEs). These models assume that the observed dynamics are driven exclusively by internal, deterministic mechanisms. However, real biological systems will always be exposed to influences that are not completely understood or not feasible to model explicitly. Ignoring these phenomena in the modeling may affect the analysis of the studied biological systems. Therefore there is an increasing need to extend the deterministic models to models that embrace more complex variations in the dynamics. A way of modeling these elements is by including stochastic influences or noise. A natural extension of a deterministic differential equations model is a system of stochastic differential equations (SDEs), where relevant parameters are modeled as suitable stochastic processes, or stochastic processes are added to the driving system equations. This approach assumes that the dynamics are partly driven by noise.

Keywords

Markov Chain Monte Carlo Wiener Process Transition Density Geometric Brownian Motion Brownian Bridge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of CopenhagenCopenhagenDenmark
  2. 2.CNRS UMR8145, Laboratoire MAP5Université Paris DescartesParisFrance

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