Related papers: The Multiple Points of Fractional Brownian Motion

We prove a conditional local limit theorem for discrete-time fractional Brownian motions (dfBm) with Hurst parameter 3/4<H<1. Using results from infinite ergodic theory it is then shown that the properly scaled occupation time of dfBm…

It is shown that the law of an SDE driven by fractional Brownian motion with Hurst parameter greater than 1/2 has a smooth density with respect to Lebesgue measure, provided that the driving vector fields satisfy H\"ormander's condition.…

Fractional Brownian motion is a self-affine, non-Markovian and translationally invariant generalization of Brownian motion, depending on the Hurst exponent $H$. Here we investigate fractional Brownian motion where both the starting and the…

Let $X$ be a (two-sided) fractional Brownian motion of Hurst parameter $H\in (0,1)$ and let $Y$ be a standard Brownian motion independent of $X$. Fractional Brownian motion in Brownian motion time (of index $H$), recently studied in…

In Ayache and Taqqu (2005), the multifractional Brownian (mBm) motion is obtained by replacing the constant parameter $H$ of the fractional Brownian motion (fBm) by a smooth enough functional parameter $H(.)$ depending on the time $t$.…

We analyze the effect of additive fractional noise with Hurst parameter $H > \frac{1}{2}$ on fast-slow systems. Our strategy is based on sample paths estimates, similar to the approach by Berglund and Gentz in the Brownian motion case. Yet,…

We study distribution dependent stochastic differential equations with irregular, possibly distributional drift, driven by an additive fractional Brownian motion of Hurst parameter $H\in (0,1)$. We establish strong well-posedness under a…

For $0<\alpha \leq 2$ and $0<H<1$, an $\alpha$-time fractional Brownian motion is an iterated process $Z = \{Z(t)=W(Y(t)), t \ge 0\}$ obtained by taking a fractional Brownian motion $\{W(t), t\in \RR{R} \}$ with Hurst index $0<H<1$ and…

Using the multiple stochastic integrals we prove an existence and uniqueness result for a linear stochastic equation driven by the fractional Brownian motion with any Hurst parameter. We study both the one parameter and two parameter cases.…

If we compose a smooth function g with fractional Brownian motion B with Hurst index H > 1/2, then the resulting change of variables formula [or It/^o- formula] has the same form as if fractional Brownian motion would be a continuous…

We study the two-dimensional fractional Brownian motion with Hurst parameter $H>{1/2}$. In particular, we show, using stochastic calculus, that this process admits a skew-product decomposition and deduce from this representation some…

We give a new representation of fractional Brownian motion with Hurst parameter H<=1/2 using stochastic partial differential equations. This representation allows us to use the Markov property and time reversal, tools which are not usually…

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.…

In this paper, we study the existence and (H\"older) regularity of local times of stochastic differential equations driven by fractional Brownian motions. In particular, we show that in one dimension and in the rough case H<1/2, the…

We prove a change of variable formula for the 2D fractional Brownian motion of index H bigger of equal to 1/4. For H strictly bigger than 1/4, our formula coincides with that obtained by using the rough paths theory. For H=1/4 (the more…

The aim of this paper is to establish the weak convergence, in the topology of the Skorohod space, of the $\nu$-symmetric Riemann sums for functionals of the fractional Brownian motion when the Hurst parameter takes the critical value…

We propose some class of statistics suitable for estimation of the Hurst index of the fractional Brownian motion based on the second order increments of an observed discrete trajectory.

We find an explicit expression for the cross-covariance between stochastic integral processes with respect to a $d$-dimensional fractional Brownian motion (fBm) $B_t$ with Hurst parameter $H>1/2$, where the integrands are vector fields…

We study the ergodic properties of finite-dimensional systems of SDEs driven by non-degenerate additive fractional Brownian motion with arbitrary Hurst parameter $H\in(0,1)$. A general framework is constructed to make precise the notions of…

We consider the problem of efficient estimation for the drift of fractional Brownian motion $B^H:=(B^H_t)_{t\in[0,T]}$ with hurst parameter $H$ less than 1/2. We also construct superefficient James-Stein type estimators which dominate,…