Stochastic Nonlinear Systems
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.
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 Google Scholar
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 Google Scholar
One-step convergence errors are discussed in
- Milstein G (1995) Numerical integration of stochastic differential equations, vol 313. Springer, Berlin Google Scholar