Markov or non-Markov property of cM-X processes

Hiroyuki MATSUMOTO; Yukio OGURA

doi:10.2969/jmsj/1191418643

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Home > Journals > J. Math. Soc. Japan > Volume 56 > Issue 2 > Article

April, 2004 Markov or non-Markov property of

cM-X

processes

Hiroyuki MATSUMOTO, Yukio OGURA

J. Math. Soc. Japan 56(2): 519-540 (April, 2004). DOI: 10.2969/jmsj/1191418643

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Abstract

For a Brownian motion with a constant drift $X$ and its maximum process $M,$ $M-X$ and $2M-X$ are diffusion processes by the extensions of Lévy's and Pitman's theorems. We show that $cM-X$ is not a Markov process if $c\in R\backslash \{0,1,2\}$ ∊ $R\backslash \{0,1,2\}$ . We also give other elementary proofs of Lévy's and Pitman's theorems.

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Hiroyuki MATSUMOTO. Yukio OGURA. "Markov or non-Markov property of $cM-X$ processes." J. Math. Soc. Japan 56 (2) 519 - 540, April, 2004. https://doi.org/10.2969/jmsj/1191418643