Related papers: Multifractional, multistable, and other processes …
Assume that a stochastic processes can be approximated, when some scale parameter gets large, by a fluid limit (also called "mean field limit", or "hydrodynamic limit"). A common practice, often called the "fixed point approximation"…
The records statistics in stationary and non-stationary fractal time series is studied extensively. By calculating various concepts in record dynamics, we find some interesting results. In stationary fractional Gaussian noises, we observe a…
This paper introduces stationary and multi-self-similar random fields which account for stochastic volatility and have type G marginal law. The stationary random fields are constructed using volatility modulated mixed moving average fields…
A fractional generalization of variations is used to define a stability of non-integer order. Fractional variational derivatives are suggested to describe the properties of dynamical systems at fractional perturbations. We formulate…
This article presents various weak laws of large numbers for the so-called realised covariation of a bivariate stationary stochastic process which is not a semimartingale. More precisely, we consider two cases: Bivariate moving average…
Brownian and fractional processes are useful computational tools for the modelling of physical phenomena. Here, modelling linear homopolymers in solution as Brownian or fractional processes, we develop a formalism to take into account both…
In this paper we study a parametric class of stochastic processes to model both fast and slow anomalous diffusion. This class, called generalized grey Brownian motion (ggBm), is made up off self-similar with stationary increments processes…
We define a time dependent empirical process based on $n$ i.i.d.~fractional Brownian motions and establish Gaussian couplings and strong approximations to it by Gaussian processes. They lead to functional laws of the iterated logarithm for…
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…
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 consider the class of stationary-increment harmonizable stable processes with infinite control measure, which most notably includes real harmonizable fractional stable motions. We give conditions for the integrability of the paths of…
Recent evidence suggests that physiological signals under healthy conditions may have a fractal temporal structure. We investigate the possibility that time series generated by certain physiological control systems may be members of a…
A recently proposed alternative to multifractional Brownian motion (mBm) with random Hurst exponent is studied, which we refer to as It\^o-mBm. It is shown that It\^o-mBm is locally self-similar. In contrast to mBm, its pathwise regularity…
Based on criteria of mathematical simplicity and consistency with empirical market data, a stochastic volatility model is constructed, the volatility process being driven by fractional noise. Price return statistics and asymptotic behavior…
The recent experimental progresses in handling microscopic systems have allowed to probe them at levels where fluctuations are prominent, calling for stochastic modeling in a large number of physical, chemical and biological phenomena. This…
The reduction of a continuous Markov process with multiple metastable states to a discrete rate process is investigated in the presence of slow time dependent parameters such as periodic external forces or slowly fluctuating barrier…
We investigated the quality of forecasting of fractional Brownian motion, and new method for estimating of Hurst exponent is validated. Stochastic model of the time series in the form of converted fractional Brownian motion is proposed. The…
Stochastic processes with temporal delay play an important role in science and engineering whenever finite speeds of signal transmission and processing occur. However, an exact mathematical analysis of their dynamics and thermodynamics is…
In this paper, we consider a continuous-time autoregressive fractionally integrated moving average (CARFIMA) model, which is defined as the stationary solution of a stochastic differential equation driven by a standard fractional Brownian…
The paper obtains the general form of the cross-covariance function of vector fractional Brownian motion with correlated components having different self-similarity indices.