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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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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DOI: https://doi.org/10.1007/PL00008733
- Mathematics Subject Classification (1991): 60J65
- Key words: Local time – modulus of continuity – large increment – Brownian motion