On the maximum of a fractional Brownian motion

Theory of Probability and its Applications

Volumn 44, Issue 1, 1999, Pages 97-102

  Molchan, G M ^a  

^a INSTITUTE OF EARTHQUAKE PREDICTION THEORY AND MATHEMATICAL GEOPHYSICS   (Russian Federation)

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Indexed keywords

EID: 0033271145     PISSN: 0040585X     EISSN: None     Source Type: Journal    
DOI: 10.1137/s0040585x97977379     Document Type: Article

References (6)

1. M. A. LIFSHITS, Gaussian Random Variables, TViMS, Kiev, 1995 (in Russian).
2. YA. G. SINAI, On the distribution of the maximum of fractional Brownian motion, Uspekhi Mat. Nauk, 52 (1997), pp. 119-138 (in Russian).
3. V. I. PITERBARG AND V. P. PRISYAZHNYUK, Asymptotic behavior of the probability of a large excursion for a nonstationary Gaussian process, Theory Probab. Math. Statist., 18 (1978), pp. 121-134 (in Russian).
4. K. KAWAZU AND H. TANAKA, On the maximum of a diffusion process in a drifted Brownian environment, in Séminaire de Probabilités XXVII, Lecture Notes in Math. 1557, Springer, Berlin, 1993, pp. 78-85.
5. X. FERNIQUE, Régularité des trajectoires des fonctions aléatoires gaussiennes, in École d'Été de Probabilités de Saint-Flour, IV-1974, Lectures Notes in Math. 480, Springer, Berlin, 1975, pp. 2-187.
6. G. M. MOLCHAN AND YU. I. GOLOSOV, Gaussian processes with asymptotically power spectrum, Dokl. Akad. Nauk SSSR, 184 (1969), pp. 546-549.