Related papers: Operator Fractional Brownian Motion and Martingale…
We introduce a variational theory for processes adapted to the multi-dimensional Brownian motion filtration. The theory provides a differential structure which describes the infinitesimal evolution of Wiener functionals at very small…
It is discussed the limitations of the widely used markovian approximation applied to model the turbulent refractive index in lightwave propagation. It is well-known the index is a passive scalar field. Thus, the actual knowledge about…
We propose a generalization of the widely used fractional Brownian motion (FBM), memory-multi-FBM (MMFBM), to describe viscoelastic or persistent anomalous diffusion with time-dependent memory exponent $\alpha(t)$ in a changing environment.…
In this paper we investigate the boundary non-crossing probabilities of a fractional Brownian motion considering some general deterministic trend function. We derive bounds for non-crossing probabilities and discuss the case of a large…
This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional…
In a recent paper, Cohl and Costas-Santos derived a number of interesting multi-derivative and multi-integral relations for associated Legendre and Ferrers functions in which the orders of those functions are changed in integral steps.…
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,…
Although fractional Brownian motion was not invented by Benoit Mandelbrot, it was he who recognized the importance of this random process and gave it the name by which it is known today. This is a personal account of the history behind…
Self-similarity is widely considered the reference framework for modeling the scaling properties of real-world data. However, most theoretical studies and their practical use have remained univariate. Operator Fractional Brownian Motion…
The martingale part in the semimartingale decomposition of a Brownian motion with respect to an enlargement of its filtration, is an anticipative mapping of the given Brownian motion. In analogy to optimal transport theory, we define causal…
For equidistant discretizations of fractional Brownian motion (fBm), the probabilities of ordinal patterns of order d=2 are monotonically related to the Hurst parameter H. By plugging the sample relative frequency of those patterns…
We present a Cameron--Martin type quasi-invariance theorem for subordinate Brownian motion. As applications, we establish an integration by parts formula and construct a gradient operator on the path space of subordinate Brownian motion,…
The $n$th order fractional Brownian motion was introduced by Perrin et al. It is the (upto a multiplicative constant) unique self-similar Gaussian process with Hurst index $H \in (n-1,n)$, having $n$th order stationary increments. We…
This paper deals with fractional-order controlled systems and fractional-order controllers in the frequency domain. The mathematical description by fractional transfer functions and properties of these systems are presented. The new ways…
Fractional differential (and difference) operators play a role in a number of diverse settings: integrable systems, mirror symmetry, Hurwitz numbers, the Bethe ansatz equations. We prove extensions of the three major results on algebras of…
In this paper, a new variant to fractional signal processing is proposed known as the Reduced Order Fractional Fourier Transform. Various properties satisfied by its transformation kernel is derived. The properties associated with the…
In this paper an arbitrage strategy is constructed for the modified Black-Scholes model driven by fractional Brownian motion or by a time changed fractional Brownian motion, when the volatility is stochastic. This latter property allows the…
Fractional classical mechanics has been introduced and developed as a classical counterpart of the fractional quantum mechanics. Lagrange, Hamilton and Hamilton-Jacobi frameworks have been implemented for the fractional classical mechanics.…
Functionals of Brownian/non-Brownian motions have diverse applications and attracted a lot of interest of scientists. This paper focuses on deriving the forward and backward fractional Feynman-Kac equations describing the distribution of…
The aim of this paper is to prove an analogue of Baxter's inequality for fractional Brownian motion-type processes with Hurst index less than 1/2. This inequality is concerned with the norm estimate of the difference between finite- and…