On the Continuity of Brownian Motion with a Multidimensional Parameter
- 1 February 1960
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 16, 135-156
- https://doi.org/10.1017/s0027763000007613
Abstract
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.Keywords
This publication has 4 references indexed in Scilit:
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- On the Uniform Continuity of Wiener Process with a Multidimensional ParameterNagoya Mathematical Journal, 1958
- On the application of the Borel-Cantelli lemmaTransactions of the American Mathematical Society, 1952
- The Law of the Iterated Logarithm for Identically Distributed Random VariablesAnnals of Mathematics, 1946