Book description
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 Finance offers a comprehensive examination to the most important issues of stochastic differential equations and their applications. The author — a noted expert in the field — includes myriad illustrative examples in modelling dynamical phenomena subject to randomness, mainly in biology, bioeconomics and finance, that clearly demonstrate the usefulness of stochastic differential equations in these and many other areas of science and technology.
The text also features reallife situations with experimental data, thus covering topics such as Monte Carlo simulation and statistical issues of estimation, model choice and prediction. The book includes the basic theory of option pricing and its effective application using reallife. The important issue of which stochastic calculus, Itô or Stratonovich, should be used in applications is dealt with and the associated controversy resolved. Written to be accessible for both mathematically advanced readers and those with a basic understanding, the text offers a wealth of exercises and examples of application. This important volume:
 Contains a complete introduction to the basic issues of stochastic differential equations and their effective application
 Includes many examples in modelling, mainly from the biology and finance fields
 Shows how to: Translate the physical dynamical phenomenon to mathematical models and back, apply with real data, use the models to study different scenarios and understand the effect of human interventions
 Conveys the intuition behind the theoretical concepts
 Presents exercises that are designed to enhance understanding
 Offers a supporting website that features solutions to exercises and R code for algorithm implementation
Written for use by graduate students, from the areas of application or from mathematics and statistics, as well as academics and professionals wishing to study or to apply these models, Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance is the authoritative guide to understanding the issues of stochastic differential equations and their application.
Table of contents
 Cover
 Preface
 About the companion website
 1 Introduction

2 Revision of probability and stochastic processes
 2.1 Revision of probabilistic concepts
 2.2 Monte Carlo simulation of random variables
 2.3 Conditional expectations, conditional probabilities, and independence
 2.4 A brief review of stochastic processes
 2.5 A brief review of stationary processes
 2.6 Filtrations, martingales, and Markov times
 2.7 Markov processes
 3 An informal introduction to stochastic differential equations
 4 The Wiener process
 5 Diffusion processes

6 Stochastic integrals
 6.1 Informal definition of the Itô and Stratonovich integrals
 6.2 Construction of the Itô integral
 6.3 Study of the integral as a function of the upper limit of integration
 6.4 Extension of the Itô integral
 6.5 Itô theorem and Itô formula
 6.6 The calculi of Itô and Stratonovich
 6.7 The multidimensional integral
 7 Stochastic differential equations
 8 Study of geometric Brownian motion (the stochastic Malthusian model or Black–Scholes model)
 9 The issue of the Itô and Stratonovich calculi
 10 Study of some functionals
 11 Introduction to the study of unidimensional Itô diffusions
 12 Some biological and financial applications
 13 Girsanov's theorem
 14 Options and the Black–Scholes formula
 15 Synthesis
 References
 Index
 End User License Agreement
Product information
 Title: Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance
 Author(s):
 Release date: April 2019
 Publisher(s): Wiley
 ISBN: 9781119166061
You might also like
book
C++ Crash Course
Upgrade your Code with C++ C++ is one of the most widely used languages for realworld …
book
Machine Learning Pocket Reference
With detailed notes, tables, and examples, this handy reference will help you navigate the basics of …
book
Grokking Algorithms
Grokking Algorithms is a friendly take on this core computer science topic. In it, you'll learn …
book
Software Engineering at Google
Today, software engineers need to know not only how to program effectively but also how to …