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In this paper, we study the $frac{1}{H}$-variation of stochastic divergence integrals $X_t = int_0^t u_s {delta}B_s$ with respect to a fractional Brownian motion $B$ with Hurst parameter $H < frac{1}{2}$. Under suitable assumptions on the process u, we prove that the $frac{1}{H}$-variation of $X$ exists in $L^1({Omega})$ and is equal to $e_H int_0^T|u_s|^H ds$, where $e_H = mathbb{E}|B_1|^H$. In the second part of the paper, we establish an integral representation for the fractional Bessel Process $|B_t|$, where $B_t$ is a $d$-dimensional fractional Brownian motion with Hurst parameter $H < frac{1}{2}$. Using a multidimensional version of the result on the $frac{1}{H}$-variation of divergence integrals, we prove that if $2dH^2 > 1$, then the divergence integral in the integral representation of the fractional Bessel process has a $frac{1}{H}$-variation equals to a multiple of the Lebesgue measure.
We derive the asymptotic behavior of weighted quadratic variations of fractional Brownian motion $B$ with Hurst index $H=1/4$. This completes the only missing case in a very recent work by I. Nourdin, D. Nualart and C. A. Tudor. Moreover, as an appli
In this paper we develop sensitivity analyses w.r.t. the long-range/memory noise parameter for solutions to stochastic differential equations and the probability distributions of their first passage times at given thresholds. Here we consider the cas
Using structures of Abstract Wiener Spaces, we define a fractional Brownian field indexed by a product space $(0,1/2] times L^2(T,m)$, $(T,m)$ a separable measure space, where the first coordinate corresponds to the Hurst parameter of fractional Brow
The past few years have witnessed increased attention to the quest for Majorana-like excitations in the condensed matter community. As a promising candidate in this race, the one-dimensional chiral Majorana edge mode (CMEM) in topological insulator-s
Generalizations of tempered fractional Brownian from single index to two indices and variable index or tempered multifractional Brownian motion are studied. Tempered fractional Brownian motion and tempered multifractional Brownian motion with variable tempering parameter are considered.