Related papers: A large deviation principle in H\"older norm for m…
In this paper, we consider a kind of fully coupled slow fast motion, in which the slow variable satisfies the non Lipschitz condition. We prove that the stochastic flow of the slow variable exists and moreover, satisfies the large deviation…
We study several important fine properties for the family of fractional Brownian motions with Hurst parameter $H$ under the $(p,r)$-capacity on classical Wiener space introduced by Malliavin. We regard fractional Brownian motions as Wiener…
This paper presents a new estimator of the global regularity index of a multifractional Brownian motion. Our estimation method is based upon a ratio statistic, which compares the realized global quadratic variation of a multifractional…
For degenerate stochastic differential equations driven by fractional Brownian motions with Hurst parameter $H>1/2$, the derivative formulas are established by using Malliavin calculus and coupling method, respectively. Furthermore, we find…
We show that the distribution of the maximum of the fractional Brownian motion $B^H$ with Hurst parameter $H\to 0$ over an $n$-point set $\tau \subset [0,1]$ can be approximated by the normal law with mean $\sqrt{\ln n}$ and variance $1/2$…
We study integral representations of random variables with respect to general H\"older continuous processes and with respect to two particular cases; fractional Brownian motion and mixed fractional Brownian motion. We prove that arbitrary…
The present article is devoted to a fine study of the convergence of renormalized weighted quadratic and cubic variations of a fractional Brownian motion $B$ with Hurst index $H$. In the quadratic (resp. cubic) case, when $H<1/4$ (resp.…
We investigate the sharp large deviation properties of the energy and the maximum likelihood estimator for the Ornstein-Uhlenbeck process driven by a fractional Brownian motion with Hurst index greater than one half.
In this paper, we consider a complex-valued d-dimensional fractional Brownian motion defined on the closure of the complex upper half-plane, called analytic fractional Brownian motion. This process has been introduced by the second author…
The large deviation principle is proved for a class of $L^2$-valued processes that arise from the coarse-graining of a random field. Coarse-grained processes of this kind form the basis of the analysis of local mean-field models in…
We study the first-passage time, the distribution of the maximum, and the absorption probability of fractional Brownian motion of Hurst parameter $H$ with both a linear and a non-linear drift. The latter appears naturally when applying…
In this paper we study the existence of a unique solution to a general class of Young delay differential equations driven by a H\"older continuous function with parameter greater that 1/2 via the Young integration setting. Then some…
Limit theorems, including the large deviation principle, are established for random point processes (fields), which describe the position distributions of the perfect boson gas in the regime of the Bose-Einstein condensation. We compare…
We prove large deviation principles for $\int_0^t \gamma(X_s)ds$, where $X$ is a $d$-dimensional self-similar Gaussian process and $\gamma(x)$ takes the form of the Dirac delta function $\delta(x)$, $|x|^{-\beta}$ with $\beta\in (0,d)$, or…
We provide the large deviation principle for higher dimensional piecewise expanding maps and by using the functional approach of Hennion and Herv\'e, slightly modified.
In this paper, we construct consistent statistical estimators of the Hurst index, volatility coefficient, and drift parameter for Bessel processes driven by fractional Brownian motion with $H<1/2$. As an auxiliary result, we also prove the…
We construct an iterated stochastic integral with fractional Brownian motion with H > 1/2. The first integrand is a deterministic function, and each successive integral is with respect to an independent fBm. We show that this symmetric…
Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the…
In this article we will present a new perspective on the variable order fractional calculus, which allows for differentiation and integration to a variable order, i.e. one differentiates (or integrates) a function along the path of a…
Let R be a symmetric a-stable Riemann-Liouville process with Hurst parameter H > 0. Consider ||.|| a translation invariant, b-self-similar, and p-pseudo-additive functional semi-norm. We show that if H > (b + 1/p) and c = (H - b - 1/p),…