Strassen theorems for a class of iterated processes

Abstract

Abstract. A general direct Strassen theorem is proved for a class of stochastic processes and applied for iterated processes such as W (Lt), where W (·) is a standard Wiener process and L. is a local time of a Lévy process independent from W (·).

Correlated continuous time random walks

“…Large deviation and modulus of continuity results for LTFBM are developed in a companion paper [26]. Strassen-type law of the iterated logarithm has been proved by Csáki, Földes and Révész [15] for local time Brownian motion (LTBM, the case H = 1/2). It is interesting to note that our Theorem 2.4 shows that "randomly-stopped stationary sequence" {(Y n : n ≤ N t ), t ≥ 0} belongs to the domain of attraction of {W H (L t ), t ≥ 0} for all H ∈ (0, 1).…”

Limit Theorems for Local and Occupation Times of Random Walks and Brownian Motion on a Spider

“…Strassen-type theorems for the IBM, that also imply limsup results, are given in Csáki et al [10], [13], and Hu et al [21]. A Chung-type liminf result is shown in Hu et al [21].…”

Some Results and Problems for Anisotropic Random Walks on the Plane

“…One of our old results [10] describes the Strassen class of η 1 (0, η 2 (0, zt)) as follows. This, combined with Theorems 3.2 and 3.…”