p-Variation of strong Markov processes

• 成果类型: Article
• 署名作者: Manstavicius, M
• 署名单位: University of Connecticut
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117904000000423
• 发表日期: 2004
• 页码: 2053-2066
• 关键词: equations

摘要

Let xit, t is an element of [0, T], be a strong Markov process with values in a complete separable metric space (X, rho) and with transition probability function P-s,P-t (x, dy), 0 less than or equal to s less than or equal to t less than or equal to T, x is an element of X. For any h is an element of [0, T] and a > 0, consider the function alpha(h,a) = sup{P-s,P-t(x, {y:rho(x,y) greater than or equal to a}):x is an element of X, 0 less than or equal to s less than or equal to t less than or equal to (s +h) boolean AND T}. It is shown that a certain growth condition on alpha(h, a), as a down arrow 0 and h stays fixed, implies the almost sure boundedness of the p-variation of xit, where p depends on the rate of growth.