We study the path behaviour of general random walks, and that of their local times, on the 2-dimensional comb lattice that is obtained from by removing all horizontal edges off the x-axis. We prove strong approximation results for such random walks and also for their local times. Concentrating...

For a simple symmetric random walk in dimension d[greater-or-equal, slanted]3, a uniform strong law of large numbers is proved for the number of sites with given local time up to time n.

We study the occupation measure of various sets for a symmetric transient random walk in Zd with finite variances. Let denote the occupation time of the set A up to time n. It is shown that tends to a finite limit as n--[infinity]. The limit is expressed in terms of the largest eigenvalue of a...

This paper is devoted to the study of the additive functional , where f denotes a measurable function and W is a planar Brownian motion. Kasahara and Kotani (Z. Wahrsch. Verw. Gebiete 49(2) (1979) 133) have obtained its second-order asymptotic behavior, by using the skew-product representation...

We prove almost sure convergence for the logarithmic average of f(W(X(t))/[psi](t)), where f is a suitable function, [psi](t) is a norming factor, W is a Wiener process and X is a suitable process, independent of W. Particular attention is paid for the case when X is the local time of a Wiener...

We study the asymptotic behaviour of the occupation time process [integral operator]t0 IA(W1(L2(s)))ds, t [greater-or-equal, slanted] 0, where W1 is a standard Wiener process and L2 is a Wiener local time process at zero that is independent from W1. We prove limit laws, as well as almost sure...

A class of iterated processes is studied by proving a joint functional limit theorem for a pair of independent Brownian motions. This Strassen method is applied to prove global (t -- [infinity]), as well as local (t -- 0), LIL type results for various iterated processes. Similar results are also...

A limit theorem is given for the quadratic variation of the local time of a random walk and that of a Wiener process.

Let L(a, t) be the local time of a Wiener process, and put . It is shown that if g(t)=t1/2(log t)-1(log log t)-1 and . A similar result is proved for random g(t) depending on the maximum of the Wiener process. These results settle a problem posed by Csörgo and Révész [7].