Existence, renormalization, and regularity properties of higher order derivatives of self-intersection local time of fractional Brownian motion

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.

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...

Regularity of Intersection Local Times of Fractional Brownian Motions

Let Bi be an (Ni, d)-fractional Brownian motion with Hurst index αi (i = 1,2), and let B1 and B2 be independent. We prove that, if N1 α1 + N2 α2 > d , then the intersection local times of B1 and B2 exist, and have a continuous version. We also establish Hölder conditions for the intersection local times and determine the Hausdorff and packing dimensions of the sets of intersection times and int...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...