Markov or non-Markov property of cM - X processes

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Author(s)

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∈ \bm{R}\backslash{0, 1, 2}. We also give other elementary proofs of Lévy's and Pitman's theorems.

Journal

  • Journal of the Mathematical Society of Japan

    Journal of the Mathematical Society of Japan 56(2), 519-540, 2004-04-01

    The Mathematical Society of Japan

References:  21

Codes

  • NII Article ID (NAID)
    10013123100
  • NII NACSIS-CAT ID (NCID)
    AA0070177X
  • Text Lang
    ENG
  • Article Type
    ART
  • ISSN
    00255645
  • NDL Article ID
    6928402
  • NDL Source Classification
    ZM31(科学技術--数学)
  • NDL Call No.
    Z53-A209
  • Data Source
    CJP  NDL  J-STAGE 
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