作者：Perman, M; Werner, W
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS)
摘要：We study 'perturbed Brownian motions', that can be, loosely speaking, described as follows: they behave exactly as linear Brownian motion except when they hit their past maximum or/and maximum where they get an extra 'push'. We define with no restrictions on the perturbation parameters a process which has this property and show that its law is unique within a certain 'natural class' of processes. In the case where both perturbations (at the maximum and at the minimum) are self-repelling, we sh...
作者：Bentkus, V; Gotze, F
摘要：Let X,X-1,X-2,... be a sequence of i.i.d. random vectors taking values in a d-dimensional real linear space R-d. Assume that EX = 0 and that X is not concentrated in a proper subspace of R-d. Let G denote a mean zero Gaussian random vector with the same covariance operator as that of X. We investigate the distributions of non-degenerate quadratic forms Q[S-N] of the normalized sums S-N = N-1/2(X-1 + ... + X-N) and show that [GRAPHICS] provided that d greater than or equal to 9 and the fourth m...
