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)


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
$$dx = a\left( {t,X} \right)dt + \sum\limits_{r = 1}^a {\sigma _r \left( {t,X} \right)dw_r \left( t \right)}$$
where X, a, σr are vectors of dimension n.


Stochastic Differential Equation Additive Noise Wiener Process Mathematical Expectation Implicit Method 
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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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