Resumen de p-variation of strong Markov processes

Martynas Manstavicius

• 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), 0≤s≤t≤T, x∈X. For any h∈[0,T] and a>0, consider the function α(h,a)=sup{Ps,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 ξt, where p depends on the rate of growth.