Unrenormalized intersection local time of Brownian motion and its local time representation

Renormalized Self - Intersection Local Time for Fractional Brownian Motion

Let B H t be a d-dimensional fractional Brownian motion with Hurst parameter H ∈ (0, 1). Assume d ≥ 2. We prove that the renor-malized self-intersection local time ℓ = T 0 t 0 δ(B H t − B H s) ds dt − E T 0 t 0 δ(B H t − B H s) ds dt exists in L 2 if and only if H < 3/(2d), which generalizes the Varadhan renormalization theorem to any dimension and with any Hurst parameter. Motivated by a resul...

Brownian Excursion Conditioned on Its Local Time

Intersection Local Time for two Independent Fractional Brownian Motions

Let B and e B be two independent, d-dimensional fractional Brownian motions with Hurst parameter H ∈ (0, 1) . Assume d ≥ 2. We prove that the intersection local time of B and e B I(BH , e BH) = Z

Regularity of Renormalized Self-intersection Local Time for Fractional Brownian Motion

Let B H t be a d-dimensional fractional Brownian motion with Hurst parameter H ∈ (0, 1). We study the regularity, in the sense of the Malliavin calculus, of the renormalized self-intersection local time ℓ = T 0 t 0 δ 0 (B H t − B H s)dsdt − E T 0 t 0 δ 0 (B H t − B H s)dsdt , where δ 0 is the Dirac delta function.

Large deviations for local time fractional Brownian motion and applications

Article history: Received 19 December 2007 Available online 9 June 2008 Submitted by M. Ledoux