The Annals of Probability

p-variation of strong Markov processes

Martynas Manstavičius

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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{Ps,t(x,{y:ρ(x,y)a}):xX,0st(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.

Article information

Source
Ann. Probab., Volume 32, Number 3 (2004), 2053-2066.

Dates
First available in Project Euclid: 14 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.aop/1089808419

Digital Object Identifier
doi:10.1214/009117904000000423

Mathematical Reviews number (MathSciNet)
MR2073185

Zentralblatt MATH identifier
1052.60058

Subjects
Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 60G17: Sample path properties 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07] 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

Keywords
Strong Markov process Markov time p-variation transition probabilities

Citation

Manstavičius, Martynas. p -variation of strong Markov processes. Ann. Probab. 32 (2004), no. 3, 2053--2066. doi:10.1214/009117904000000423. https://projecteuclid.org/euclid.aop/1089808419


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