Increase of stable processes |
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Authors: | Jean Bertoin |
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Affiliation: | (1) Laboratoire de Probabilités (C.N.R.S.), Université Pierre et Marie Curie, 4, Place Jussieu tour 56, 3ème étage, 75252 Paris Cedex 05, France |
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Abstract: | One says thatt>0 is an increase time for a real-valued path if stays above the level (t) immediately after timet, and below (t) immediately before timet. Dvoretzkyet al.,(10) proved that Brownian motion has no increase times a.s. This result is extended here to (strictly) stable processes. Specifically, the probability that a stable processX possesses increase times is 0 if and only ifP(X1 0) 1/2. |
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Keywords: | Stable process increase points |
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