T. M. Lewis, A self--normalized law of the iterated logarithm for random walk in random scenery, J. Theor. Prob., 5 (4) (1992) 629--659. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
A Law Of The Iterated Logarithm For Stable Processes In.. - Khoshnevisan, Lewis (1998) (2 citations) Self-citation (Lewis) (Correct)
....: 1:7) Thus, normalized random walk in random scenery converges in distribution to a stable process in random scenery. For additional information on random walks in random scenery and stable processes in random scenery, see Bolthausen (1989) Kesten and Spitzer (1979) Lang and Nguyen (1983) Lewis (1992), Lewis (1993) Lou (1985) and R emillard and Dawson (1991) Viewing (1.7) as the central limit theorem for random walk in random scenery, it is natural to investigate the law of the iterated logarithm, which would describe the asymptotic behavior of g n as n 1: To give one such result, for each ....
....To give one such result, for each n 0 let v n = X a2Z Gamma a n Delta 2 : The process V = fv n : n 0g is called the self intersection local time of the random walk. Throughout this paper, we will write log e to denote the natural logarithm. For x 2 R; define ln(x) log e (x e) In Lewis (1992), it has been shown that if E jy(0)j 3 1, then lim sup n 1 g n p 2v n ln ln(n) 1; a.s. 3 This is called a self normalized law of the iterated logarithm in that the rate of growth of g n as n 1 is described by a random function of the process itself. The goal of this article is ....
T. M. Lewis, A self--normalized law of the iterated logarithm for random walk in random scenery, J. Theor. Prob., 5 (4) (1992) 629--659.
Stochastic Calculus for Brownian Motion on a Brownian Fracture - Khoshnevisan, Lewis (1997) Self-citation (Lewis) (Correct)
.... by the connection between the quadratic variation of iterated Brownian motion and the stochastic process called Brownian motion in random scenery, first described and studied in [27] Since the introduction of this model, various aspects of Brownian motion in random scenery have been studied in [7, 31, 32, 33, 34, 36], We will use the following notation in the sequel. Let DR [0; 1] denote the space of real valued functions on [0; 1] which are right continuous and have left hand limits. Given random elements fT n g and T in DR [0; 1] we will write T n = T to denote the convergence in distribution of the fT ....
T. M. Lewis (1992), A self-normalized law of the iterated logarithm for random walk in random scenery. J. Theoret. Probab. 5(4), 629--659.
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