Related papers: Persistence probabilities of a smooth self-similar…

We study the two-dimensional overdamped motion of an active particle whose orientational dynamics is subject to fractional Brownian noise, whereas its position is affected by self-propulsion and Brownian fluctuations. From a Langevin-like…

We investigate the asymptotic behavior as time goes to infinity of Hawkes processes whose regression kernel has $L^1$ norm close to one and power law tail of the form $x^{-(1+\alpha)}$, with $\alpha\in(0,1)$. We in particular prove that…

We introduce a class of Gaussian processes with stationary increments which exhibit long-range dependence. The class includes fractional Brownian motion with Hurst parameter H>1/2 as a typical example. We establish infinite and finite past…

The characteristic feature of semi-selfsimilar process is the invariance of its finite dimensional distributions by certain dilation for specific scaling factor. Estimating the scale parameter $\lambda$ and the Hurst index of such processes…

We study the diffusive motion of a particle in a subharmonic potential of the form $U(x)=|x|^c$ ($0<c<2$) driven by long-range correlated, stationary fractional Gaussian noise $\xi_{\alpha}(t)$ with $0<\alpha\le2$. In the absence of the…

In this paper we estimate both the Hurst and the stable indices of a H-self-similar stable process. More precisely, let $X$ be a $H$-sssi (self-similar stationary increments) symmetric $\alpha$-stable process. The process $X$ is observed at…

We introduce fractional diffusion Bessel process with Hurst index $H\in(0,\frac12)$, derive a stochastic differential equation for it, and study the asymptotic properties of its sample paths.

For an arbitrary diffusion process $X$ with time-homogeneous drift and variance parameters $\mu(x)$ and $\sigma^2(x)$, let $V_\varepsilon$ be $1/\varepsilon$ times the total time $X(t)$ spends in the strip…

In Chen and Zhou 2021, they consider an inference problem for an Ornstein-Uhlenbeck process driven by a general one-dimensional centered Gaussian process $(G_t)_{t\ge 0}$. The second order mixed partial derivative of the covariance function…

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),…

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…

The (fractional) Brownian sheet is a simplest example of a Gaussian random field X whose covariance is the tensor product of a finite number (d) of nonnegative correlation functions of self-similar Gaussian processes. Let Y be the…

We study the persistence probabilities of a moving average process of order one with innovations that follow a Laplace distribution. The persistence probabilities can be computed fully explicitly in terms of classical combinatorial…

This paper derives the Fokker-Planck (FP) equation for a particle moving in potential by a randomly modulated dipole. The FP equation describes the anomalous diffusion observed in the companion paper [1] and breaks the conservation of the…

Since the middle of the 90's, multifractional processes have been introduced for overcoming some limitations of the classical Fractional Brownian Motion model. In their context, the Hurst parameter becomes a Holder continuous function H(?)…

A possible mechanism leading to anomalous diffusion is the presence of long-range correlations in time between the displacements of the particles. Fractional Brownian motion, a non-Markovian self-similar Gaussian process with stationary…

Let $v:[0,T]\times \R^d \to \R$ be the solution of the parabolic backward equation $ \partial_t v + (1/2) \sum_{i,l} [\sigma \sigma^\perp]_{il} \partial_{x_i \partial_{x_l} v + \sum_{i} b_i \partial_{x_i}v + kv =0$ with terminal condition…

We develop and investigate a test for jumps based on high-frequency observations of a fractional process with an additive jump component. The Hurst exponent of the fractional process is unknown. The asymptotic theory under infill…

We derive a higher-order asymptotic expansion of the conditional characteristic function of the increment of an It\^o semimartingale over a shrinking time interval. The spot characteristics of the It\^o semimartingale are allowed to have…

The molecular motion in heterogeneous media displays anomalous diffusion by the mean-squared displacement $\langle X^2(t) \rangle = 2 D t^\alpha$. Motivated by experiments reporting populations of the anomalous diffusion parameters $\alpha$…