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Increment sizes of the principal value of Brownian local time
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  • Published: August 2000

Increment sizes of the principal value of Brownian local time

  • Endre Csáki1,
  • Miklós Csörgő2,
  • Antónia Földes3 &
  • …
  • Zhan Shi4 

Probability Theory and Related Fields volume 117, pages 515–531 (2000)Cite this article

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Abstract.

Let W be a standard Brownian motion, and define Y(t)= ∫0 t ds/W(s) as Cauchy's principal value related to local time. We determine: (a) the modulus of continuity of Y in the sense of P. Lévy; (b) the large increments of Y.

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Authors and Affiliations

  1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, P.O.B. 127, H-1364, Budapest, Hungary. e-mail: csaki@math-inst.hu, , , , , , HU

    Endre Csáki

  2. School of Mathematics and Statistics, Carleton University, Ottawa, Ontario K1S 5B6, Canada. e-mail: mcsorgo@math.carleton.ca, , , , , , CA

    Miklós Csörgő

  3. College of Staten Island, CUNY, 2800 Victory Blvd., Staten Island, New York 10314, USA. e-mail: afoldes@email.gc.cuny.edu, , , , , , US

    Antónia Földes

  4. Laboratoire de Probabilités UMR 7599, Université Paris VI, 4 Place Jussieu, F-75252 Paris Cedex 05, France. e-mail: zhan@proba.jussieu.fr, , , , , , FR

    Zhan Shi

Authors
  1. Endre Csáki
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  2. Miklós Csörgő
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  3. Antónia Földes
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  4. Zhan Shi
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Additional information

Received: 1 April 1999 / Revised version: 27 September 1999 / Published online: 14 June 2000

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Csáki, E., Csörgő, M., Földes, A. et al. Increment sizes of the principal value of Brownian local time. Probab Theory Relat Fields 117, 515–531 (2000). https://doi.org/10.1007/PL00008733

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  • Issue Date: August 2000

  • DOI: https://doi.org/10.1007/PL00008733

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  • Mathematics Subject Classification (1991): 60J65
  • Key words: Local time – modulus of continuity – large increment – Brownian motion
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