Abstract
In this chapter we extend the ideas of Chap. 16 to the nonlinear case. We first describe aspects of nonlinear stochastic models based on stochastic calculus. Important technical issues arise such as the Ito rule and Ito-Taylor expansions for stochastic processes. These ideas are applied to numerical solutions of stochastic differential equations.
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Further Reading
A comprehensive introduction to stochastic differential equations can be found in
Øksendal B (2003) Stochastic differential equations. An introduction with applications, 6th edn. Springer, Berlin
A comprehensive treatment of the solution of nonlinear stochastic differential equations, including fixed-time local and fixed-time global convergence errors, is available in
Kloeden PE, Platen E (1992) Numerical solution of stochastic differential equations. Springer, Berlin
One-step convergence errors are discussed in
Milstein G (1995) Numerical integration of stochastic differential equations, vol 313. Springer, Berlin
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Yuz, J.I., Goodwin, G.C. (2014). Stochastic Nonlinear Systems. In: Sampled-Data Models for Linear and Nonlinear Systems. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-5562-1_17
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DOI: https://doi.org/10.1007/978-1-4471-5562-1_17
Publisher Name: Springer, London
Print ISBN: 978-1-4471-5561-4
Online ISBN: 978-1-4471-5562-1
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