Unilateral small deviations of processes related to the fractional Brownian motion

Stochastic Processes and their Applications - Tập 118 - Trang 2085-2097 - 2008
G. Molchan

Tài liệu tham khảo

Csáki, 2000, Boundary crossings and the distribution function of the maximum of Brownian sheet, Stochastic Process. Appl., 90, 1, 10.1016/S0304-4149(00)00031-4 Fernique, 1975, Regularite des trajectoires des functions aleatoires gaussiennes, Lectures Notes in Math., 480, 2 Falconer, 1995 Kim, 1990, Cube root asymptotics, The Annals of Statistics, 18, 191, 10.1214/aos/1176347498 Ledoux, 1991 Li, 2004, Lower tail probabilities for Gaussian processes, Ann. Probab., 32, 216, 10.1214/aop/1078415834 Lifshits, 1995 Majumdar, 1999, Persistence in nonequilibrium systems, Current Sci., 77, 370 Molchan, 1999, Maximum of a fractional Brownian motion: Probabilities of small values, Commun. Math. Phys., 205, 97, 10.1007/s002200050669 Molchan, 2001, On a maximum of stable Levy processes, Theory Probab. Appl., 45, 343, 10.1137/S0040585X97978294 Molchan, 2004, Small values of the maximum for the integral of fractional Brownian motion, J. Stat. Phys., 114, 923, 10.1023/B:JOSS.0000012512.18060.a5 Molchan, 2002, A stochastic model of sedimentation: Probabilities and multifractality, Euro. J. Appl. Math., 13, 371, 10.1017/S0956792502004850 G. Molchan, A. Khokhlov, Unilateral small deviations for the integral of fractional Brownian motion. Arxiv:math.PR/0310413 (2003) Sinai, 1992, Distribution of some functionals of the integral of a random walk, Theor. Math. Phys., 90, 219, 10.1007/BF01036528