Stochastic Biomathematical Models

Stochastic biomathematical models are becoming increasingly important as new light is shed on the role of noise in living systems. In certain biological systems, stochastic effects may even enhance a signal, thus providing a biological motivation for the noise observed in living systems. Recent advances in stochastic analysis and increasing computing power facilitate the analysis of more biophysically realistic models, and this book provides researchers in computational neuroscience and stochastic systems with an overview of recent developments. Key concepts are developed in chapters written by experts in their respective fields. Topics include: one-dimensional homogeneous diffusions and their boundary behavior, large deviation theory and its application in stochastic neurobiological models, a review of mathematical methods for stochastic neuronal integrate-and-fire models, stochastic partial differential equation models in neurobiology, and stochastic modeling of spreading cortical depression.

Written by current leading experts in the field Focus on interdisciplinary (physiological and biological) applications of stochastic methods Representation of key theoretical ideas but also clear and motivated examples of application and implementation issues Includes supplementary material: sn.pub/extras

Inhalt
1 Introduction to stochastic models in biology.- 2 One-dimensional homogeneous diffusions.- 3 A brief introduction to large deviations theory.- 4 Some numerical methods for rare events simulation and analysis.- 5 Stochastic Integrate and Fire models: a review on mathematical methods and their applications.- 6 Stochastic partial differential equations in Neurobiology: linear and nonlinear models for spiking neurons.- 7 Deterministic and stochastic FitzHugh-Nagumo systems.- 8 Stochastic modeling of spreading cortical depression