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Mean-square approximation of solutions of systems of stochastic differential equations

  • G. N. Milstein
Part of the Mathematics and Its Applications book series (MAIA, volume 313)

Abstract

Let (Ω, F, P) be a probability space, let F t , t 0tt 0 + T, be a nonincreasing family of σ-subalgebras of F, and let (w r(t), F t ), r = 1,...,q, be independent Wiener processes. Consider the system of stochastic differential equations in the sense of Itô
$$dx = a\left( {t,X} \right)dt + \sum\limits_{r = 1}^a {\sigma _r \left( {t,X} \right)dw_r \left( t \right)}$$
(1.1)
where X, a, σr are vectors of dimension n.

Keywords

Stochastic Differential Equation Additive Noise Wiener Process Mathematical Expectation Implicit Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • G. N. Milstein
    • 1
  1. 1.Department of MathematicsUral State UniversityEkatarinburgRussia

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