Modeling of Itô integrals

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


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 .


Stochastic Differential Equation Wiener Process Fourier Method Trapezium Method Approximate Identity 
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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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