Stochastic Biomathematical Models: with Applications to Neuronal Modeling

✍ Scribed by Susanne Ditlevsen, Adeline Samson (auth.), Mostafa Bachar, Jerry Batzel, Susanne Ditlevsen (eds.)

Publisher: Springer-Verlag Berlin Heidelberg
Year: 2013
Tongue: English
Leaves: 215
Series: Lecture Notes in Mathematics 2058
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xvi
Front Matter....Pages 1-1
Introduction to Stochastic Models in Biology....Pages 3-35
One-Dimensional Homogeneous Diffusions....Pages 37-55
A Brief Introduction to Large Deviations Theory....Pages 57-72
Some Numerical Methods for Rare Events Simulation and Analysis....Pages 73-95
Front Matter....Pages 97-97
Stochastic Integrate and Fire Models: A Review on Mathematical Methods and Their Applications....Pages 99-148
Stochastic Partial Differential Equations in Neurobiology: Linear and Nonlinear Models for Spiking Neurons....Pages 149-173
Deterministic and Stochastic FitzHugh–Nagumo Systems....Pages 175-186
Stochastic Modeling of Spreading Cortical Depression....Pages 187-200
Back Matter....Pages 201-206

✦ Subjects

Probability Theory and Stochastic Processes; Mathematical Modeling and Industrial Mathematics; Statistics for Life Sciences, Medicine, Health Sciences; Neurobiology

📜 SIMILAR VOLUMES

Stochastic Neuron Models

📁 Stochastic Neuron Models

✍ Priscilla E. Greenwood, Lawrence M. Ward (auth.) 📂 Library 📅 2016 🏛 Springer International Publishing 🌐 English

This book describes a large number of open problems in the theory of stochastic neural systems, with the aim of enticing probabilists to work on them. This includes problems arising from stochastic models of individual neurons as well as those arising from stochastic models of the activities of s

Stochastic Differential Models With Appl

📁 Stochastic Differential Models With Applications To Physiology (Ph.D. dissertation)

✍ Umberto Picchini 📂 Library 📅 2006 🌐 English

Introduction to Stochastic Calculus Appl

📁 Introduction to Stochastic Calculus Applied to Finance (Stochastic Modeling)

✍ Damien Lamberton, Bernard Lapeyre, 📂 Library 📅 1996 🌐 English

In recent years the growing importance of derivative products financial markets has increased financial institutions' demands for mathematical skills. This book introduces the mathematical methods of financial modeling with clear explanations of the most useful models. Introduction to Stochastic Cal

Models of the Stochastic Activity of Neu

📁 Models of the Stochastic Activity of Neurones

✍ Dr. Arun Vivian Holden (auth.) 📂 Library 📅 1976 🏛 Springer-Verlag Berlin Heidelberg 🌐 English

These notes have grown from a series of seminars given at Leeds between 1972 and 1975. They represent an attempt to gather together the different kinds of model which have been proposed to account for the stochastic activity of neurones, and to provide an introduction to this area of mathematical

Modeling with Itô Stochastic Differentia

📁 Modeling with Itô Stochastic Differential Equations (Mathematical Modelling: Theory and Applications)

✍ E. Allen 📂 Library 📅 2007 🏛 Springer 🌐 English

This book explains a procedure for constructing realistic stochastic differential equation models for randomly varying systems in biology, chemistry, physics, engineering, and finance. Introductory chapters present the fundamental concepts of random variables, stochastic processes, stochastic integr

Introduction to Stochastic Differential

📁 Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance

✍ Carlos A. Braumann 📂 Library 📅 2019 🏛 Wiley 🌐 English

A comprehensive introduction to the core issues of stochastic differential equations and their effective application Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Financeoffers a comprehensive examination to the most importan