Related papers: Wavelet estimation for operator fractional Brownia…
Wavelet based algorithms in numerical analysis are similar to other transform methods in that vectors and operators are expanded into a basis and the computations take place in this new system of coordinates. However, due to the recursive…
Fractional Brownian motion is a non-Markovian Gaussian process indexed by the Hurst exponent $H\in [0,1]$, generalising standard Brownian motion to account for anomalous diffusion. Functionals of this process are important for practical…
We consider the pricing problem related to payoffs that can have discontinuities of polynomial growth. The asset price dynamic is modeled within the Black and Scholes framework characterized by a stochastic volatility term driven by a…
At long times, a fractional Brownian particle in a confining external potential reaches a non-equilibrium (non-Boltzmann) steady state. Here we consider scale-invariant power-law potentials $V(x)\sim |x|^m$, where $m>0$, and employ the…
We report in this paper a thorough study on the the dynamical mechanics of the fractional Brownian motion systems. Where several non-trivial properties are revealed such as the abundant non-Markovian effects resulted from the fractional…
We propose a new class of rough stochastic volatility models obtained by modulating the power-law kernel defining the fractional Brownian motion (fBm) by a logarithmic term, such that the kernel retains square integrability even in the…
We introduce the concept of finite $\gamma$-scaled quadratic variation along a sequence of partitions for paths on a given interval. This concept, with historical roots in the study of Gaussian processes by Gladyshev (1961) and Klein \&…
We construct in this article a rough path over fractional Brownian motion with arbitrary Hurst index by (i) using the Fourier normal ordering algorithm introduced in \cite{Unt-Holder} to reduce the problem to that of regularizing tree…
Fractional Brownian motions(fBMs) are not semimartingales so the classical theory of It\^o integral can't apply to fBMs. Wick integration as one of the applications of Malliavin calculus to stochastic analysis is a fine definition for fBMs.…
We investigate the Local Asymptotic Property for fractional Brownian models based on discrete observations contaminated by a Gaussian moving average process. We consider both situations of low and high-frequency observations in a unified…
We study the motion of a random walker in one longitudinal and d transverse dimensions with a quenched power law correlated velocity field in the longitudinal x-direction. The model is a modification of the Matheron-de Marsily (MdM) model,…
We estimate the Hurst parameter $H$ of a fractional Brownian motion from discrete noisy data observed along a high frequency sampling scheme. The presence of systematic experimental noise makes recovery of $H$ more difficult since relevant…
This paper presents an efficient numerical technique for solving multi-dimensional fractional optimal control problems using fractional-order generalized Bernoulli wavelets. The numerical results obtained by this method have been compared…
The generalized fractional Brownian motion is a Gaussian self-similar process whose increments are not necessarily stationary. It appears in applications as the scaling limit of a shot noise process with a power law shape function and…
Fractional Levy motion (fLm) is the natural generalization of fractional Brownian motion in the context of self-similar stochastic processes and stable probability distributions. In this paper we give an explicit derivation of the…
We give a simple technic to derive the Berry-Ess\'een bounds for the quadratic variation of the subfractional Brownian motion (subfBm). Our approach has two main ingredients: ($i$) bounding from above the covariance of quadratic variation…
We investigate here the Central Limit Theorem of the Increment Ratio Statistic of a multifractional Brownian motion, leading to a CLT for the time varying Hurst index. The proofs are quite simple relying on Breuer-Major theorems and an…
This paper consider the LAN property for the mixed O-U process under high-frequency observation when H>3/4. As considered in mixed fractional Brownian motion, we will also use the projection step to get the non-diagonal rate matrix.
It has been shown recently that the optimal fluctuation method -- essentially geometrical optics -- provides a valuable insight into large deviations of Brownian motion. Here we extend the geometrical optics formalism to two-sided,…
Fractional Brownian motion has become a standard tool to address long-range dependence in financial time series. However, a constant memory parameter is too restrictive to address different market conditions. Here we model the price…