Introduction to stochastic models in biology
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Introduction to stochastic models in biology. / Ditlevsen, Susanne; Samson, Adeline.
Stochastic Biomathematical Models: with Applications to Neuronal Modeling. red. / Mostafa Bachar; Jerry Batzel; Susanne Ditlevsen. Berlin : Springer, 2013. s. 3-34 (Lecture Notes in Mathematics; Nr. 2058).Publikation: Bidrag til bog/antologi/rapport › Bidrag til bog/antologi › Forskning › fagfællebedømt
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TY - CHAP
T1 - Introduction to stochastic models in biology
AU - Ditlevsen, Susanne
AU - Samson, Adeline
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
U2 - 10.1007/978-3-642-32157-3_1
DO - 10.1007/978-3-642-32157-3_1
M3 - Book chapter
SN - 978-3-642-32156-6
T3 - Lecture Notes in Mathematics
SP - 3
EP - 34
BT - Stochastic Biomathematical Models
A2 - Bachar, Mostafa
A2 - Batzel, Jerry
A2 - Ditlevsen, Susanne
PB - Springer
CY - Berlin
ER -
ID: 16890617