Markov or non-Markov property of cM-X processes

• MATSUMOTO Hiroyuki

  Graduate School of Human Informatics Nagoya University

• OGURA Yukio

  Department of Mathematics Saga University

抄録

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.

収録刊行物

• Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ

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

  一般社団法人 日本数学会

キーワード

• Markov property
• Brownian motion
• Lévy's theorem
• Pitman's theorem

詳細情報

• CRID: 1390282680091880960
• NII論文ID: 10013123100
• NII書誌ID: AA0070177X
• DOI: 10.2969/jmsj/1191418643
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• MRID: 2048472
• NDL書誌ID: 6928402
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I6928402
• 本文言語コード: en
• データソース種別:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• 抄録ライセンスフラグ: 使用不可