On Wiener process sample paths
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- by G. J. Foschini and R. K. Mueller PDF
- Trans. Amer. Math. Soc. 149 (1970), 89-93 Request permission
Abstract:
Let $\{ {X_t}(\omega )\}$ represent a version of the Wiener process having almost surely continuous sample paths on $( - \infty ,\infty )$ that vanish at zero. We present a theorem concerning the local nature of the sample paths. Almost surely the local behavior at each t is of one of seven varieties thus inducing a partition of $( - \infty ,\infty )$ into seven disjoint Borel sets of the second class. The process $\{ {X_t}(\omega )\}$ can be modified so that almost surely the sample paths are everywhere locally recurrent.References
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Additional Information
- © Copyright 1970 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 149 (1970), 89-93
- MSC: Primary 60.62
- DOI: https://doi.org/10.1090/S0002-9947-1970-0258129-2
- MathSciNet review: 0258129