# Modeling with Itô Stochastic Differential Equations

Part of the Mathematical Modelling: Theory and Applications book series (MMTA, volume 22)

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Part of the Mathematical Modelling: Theory and Applications book series (MMTA, volume 22)

Dynamical systems with random influences occur throughout the physical, biological, and social sciences. By carefully studying a randomly varying system over a small time interval, a discrete stochastic process model can be constructed. Next, letting the time interval shrink to zero, an Ito stochastic differential equation model for the dynamical system is obtained.

This modeling procedure is thoroughly explained and illustrated for randomly varying systems in population biology, chemistry, physics, engineering, and finance. Introductory chapters present the fundamental concepts of random variables, stochastic processes, stochastic integration, and stochastic differential equations. These concepts are explained in a Hilbert space setting which unifies and simplifies the presentation. Computer programs, given throughout the text, are useful in solving representative stochastic problems. Analytical and computational exercises are provided in each chapter that complement the material in the text.

*Modeling with Itô Stochastic Differential Equations *is useful for researchers and graduate students. As a textbook for a graduate course, prerequisites include probability theory, differential equations, intermediate analysis, and some knowledge of scientific programming.

Probability theory Random variable Stochastic processes dynamische Systeme model modeling programming stochastic stochastic process

- DOI https://doi.org/10.1007/978-1-4020-5953-7
- Copyright Information Springer 2007
- Publisher Name Springer, Dordrecht
- eBook Packages Mathematics and Statistics
- Print ISBN 978-1-4020-5952-0
- Online ISBN 978-1-4020-5953-7
- Series Print ISSN 1386-2960
- Buy this book on publisher's site