Asymptotically optimum quadrature formulae for stochastic integrals

1 December 1984

conference paper
Published by Institute of Electrical and Electronics Engineers (IEEE)

p. 712-715
https://doi.org/10.1109/cdc.1984.272103

Abstract

Quadrature formulae are given for the calculation of stochastic integrals of the form ⎰f0 1(t,Wt)dt and ⎰g0 1(t,Wt) ⎰ dWt, based on measurements of a Brownian motion Wt taken at points of a regular partition. For the first a trapezoidal rule suffices; for the second a five-point formula is required. The approximation sequences these formulae generate have asymptotically optimum properties for almost every path of Wt.

Keywords

STOCHASTIC PROCESSES
MOTION CONTROL
TELLURIUM

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