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On the Continuity of Brownian Motion with a Multidimensional Parameter

Published online by Cambridge University Press:  22 January 2016

Tunekiti Sirao
Tunekiti Sirao*
Affiliation:
Shizuoka University
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A stochastic process X(A, ω) is called Brownian motion with an N-dimensional parameter when it satisfies the following conditions:

1) For any positive integer n and any set of points A1, A2, …, An in an N-dimensional Euclidian space EN, the joint variable is subject to an n-dimensional Gaussian distribution having the vector 0 as its mean vector.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 16 , February 1960 , pp. 135 - 156
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1960

References

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