Advances and Applications in Statistics
Volume 10, Issue 2, Pages 155 - 177
(December 2008)
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CONVERGENCE OF STOCHASTIC INTEGRALS AND SDE’S ASSOCIATED TO APPROXIMATIONS OF THE GAUSSIAN WHITE NOISE
Jorge Garcia (USA)
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Abstract: The Gaussian white noise in d dimensions is approximated in a
smooth way by a process We which happens to be a semimartingale
random measure. Using this approximation, the integral of an associated process
to We is taken with respect to We and also the limit of these
integrals is taken as e approaches
zero. A Wong and Zakai factor is obtained in the limit. This result is the
analogous of a time-smooth approximation of the Brownian motion. Finally, an
application to convergence of SDE’s is given, the limit of a sequence of
solutions to a stochastic differential equation is taken and the limit is
analyzed. |
Keywords and phrases: stochastic integrals, approximation Gaussian white noise, time and space, convergence, Wong-Zakai correction factor. |
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