p -variation of strong Markov processes

Manstavičius, Martynas

Ann. Probab., Tome 32 (2004) no. 1A, p. 2053-2066 / Harvested from Project Euclid

Résumé

Let ξ_t, t∈[0,T], be a strong Markov process with values in a complete separable metric space (X,ρ) and with transition probability function P_s,t(x,dy), 0≤s≤t≤T, x∈X. 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 a↓0 and h stays fixed, implies the almost sure boundedness of the p-variation of ξ_t, where p depends on the rate of growth.

Détail

Publié le : 2004-07-14
Classification:  Strong Markov process,  Markov time,  p-variation,  transition probabilities,  60J25,  60G17,  60J35,  60G40