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July 2004 p-variation of strong Markov processes
Martynas Manstavičius
Ann. Probab. 32(3): 2053-2066 (July 2004). DOI: 10.1214/009117904000000423

Abstract

Let ξt, t[0,T], be a strong Markov process with values in a complete separable metric space (X,ρ) and with transition probability function Ps,t(x,dy), 0stT, xX. For any h[0,T] and a>0, consider the function $$α(h,a)=\sup\{P_{s,t}(x,\{y:ρ(x,y)≥a\}):x∈X,0≤s≤t≤(s+h)∧T\}.$$ It is shown that a certain growth condition on α(h,a), as a0 and h stays fixed, implies the almost sure boundedness of the p-variation of ξt, where p depends on the rate of growth.

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Martynas Manstavičius. "p-variation of strong Markov processes." Ann. Probab. 32 (3) 2053 - 2066, July 2004. https://doi.org/10.1214/009117904000000423

Information

Published: July 2004
First available in Project Euclid: 14 July 2004

zbMATH: 1052.60058
MathSciNet: MR2073185
Digital Object Identifier: 10.1214/009117904000000423

Subjects:
Primary: 60J25
Secondary: 60G17 , 60G40 , 60J35

Keywords: Markov time , p-variation , strong Markov process , transition probabilities

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.32 • No. 3 • July 2004
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