Precise asymptotics in laws of the iterated logarithm for Wiener local time
نویسندگان
چکیده
In this paper, we study the asymptotic properties of the upper and lower tail probabilities of the maximum local time L∗(t) of Wiener process (Brownian motion), and obtain some precise asymptotics in the law of the iterated logarithm and the Chungs-type laws of the iterated logarithm for the supremum of Wiener local time L(x; t); x∈R; t ∈R+. c © 2003 Elsevier B.V. All rights reserved. MSC: 60F17; 60G15
منابع مشابه
Some asymptotic properties of the local timeof the uniform empirical process
We study the almost sure asymptotic properties of the local time of the uniform empirical process. In particular, we obtain two versions of the iterated logarithm law for the integral of the square of the local time. It is interesting to note that the corresponding problems for the Wiener process remain open. Properties of L p-norms of the local time are studied. We also characterize the joint ...
متن کاملStrong approximations of three-dimensional Wiener sausages
In this paper we prove that the centered three-dimensional Wiener sausage can be strongly approximated by a one-dimensional Brownian motion running at a suitable time clock. The strong approximation gives all possible laws of iterated logarithm as well as the convergence in law in terms of process for the normalized Wiener sausage. The proof relies on Le Gall [10]’s fine L-norm estimates betwee...
متن کاملModerate deviations and laws of the iterated logarithm for the volume of the intersections of Wiener sausages
Using the high moment method and the Feynman-Kac semigroup technique, we obtain moderate deviations and laws of the iterated logarithm for the volume of the intersections of two and three dimensional Wiener sausages.
متن کاملTwo different kinds of liminfs on the LIL for two-parameter Wiener processes
Some probability inequalities are obtained, and some liminf results are established for a two.parameter Wiener process by using these inequalities. The results obtained improve those of Lacey (1989) and get the watershed between the Chung type laws of the iterated logarithm and the Lacey type laws of the iterated logarithm.
متن کاملA Problem of Földes and Puri on the Wiener Process
Let W be a real-valued Wiener process starting from 0, and τ(t) be the right-continuous inverse process of its local time at 0. Földes and Puri [3] raise the problem of studying the almost sure asymptotic behavior of X(t) = ∫ τ(t) 0 1l{|W (u)|≤αt}du as t tends to infinity, i.e. they ask: how long does W stay in a tube before “crossing very much” a given level? In this note, both limsup and limi...
متن کامل