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Modeling of Itô integrals

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

Abstract

In the numerical integration formulas used in the Taylor-type expansion of solutions of systems of stochastic equations (see §2) the repeated Itô integrals
$$I_{i1, \cdots,i_j } = \int\limits_t^{t + h} {dw_{i_j } \left( \theta \right)\int\limits_t^\theta {dw_{i_{j - 1} } \left( {\theta _1 } \right)} \int\limits_t^{\theta _1 } \cdots \int\limits_t^{\theta _{j - 2} } {dw_{i_1 } \left( {\theta _{j - 1} } \right)} }$$
appeared, where i 1,…, i j take values from the set {0,1,…, q}, and dw 0(θ r) is understood to mean r .

Keywords

Stochastic Differential Equation Wiener Process Fourier Method Trapezium Method Approximate Identity 
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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