Unilateral small deviations of processes related to the fractional Brownian motion
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