We define renormalized intersection local times for random interlacements of Lévy processes in Rd and prove an isomorphism theorem relating renormalized intersection local times with associated Wick polynomials.

We establish a Tanaka-like formula relating the local times of r and r + 1 fold self-intersections of a Brownian path in the plane.

Let G={G(x),x[set membership, variant]R1} be a mean zero Gaussian process with stationary increments and set [sigma]2(x-y)=E(G(x)-G(y))2. Let f be a symmetric function with Ef2([eta])[infinity], where [eta]=N(0,1). When [sigma]2(s) is concave or when [sigma]2(s)=sr, 1r=3/2, where...

We introduce the concept of capacitary modulus for a set , which is a function h that provides simple estimates for the capacity of [Lambda] with respect to an arbitrary kernel f, estimates which depend only on the L2 inner product (h,f). We show that for a large class of Lévy processes, which...

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...

We study the object formally defined as where Xt denotes the symmetric stable processes of index 0[beta]=2 in Rd. When , this has to be defined as a limit, in the spirit of renormalized self-intersection local time. We obtain results about the large deviations and laws of the iterated logarithm...

Let G={G(x),x=0} be a mean zero Gaussian process with stationary increments and set [sigma]2(x-y)=E(G(x)-G(y))2. Let f be a function with Ef2([eta])<[infinity], where [eta]=N(0,1). When [sigma]2 is regularly varying at zero and is locally integrable for some integer j0>=1, and satisfies some additional regularity conditions, in L2. Here Hj is the jth Hermite polynomial. Also :(G')j:(I[a,b]) is a jth order Wick...</[infinity],>

We show how to renormalize the intersection local time of fractional Brownian motion of index [beta] in the plane, when½< [beta] <¾. When[beta] = ½, i.e., planar Brownian, such a renormalization is due to Varadhan.