Related papers: Continuous-time locally stationary time series mod…
We consider a generalization of a one-dimensional stochastic process known in the physical literature as L\'evy-Lorentz gas. The process describes the motion of a particle on the real line in the presence of a random array of marked points,…
Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…
The spectral theory for weakly stationary processes valued in a separable Hilbert space has known renewed interest in the past decade. Here we follow earlier approaches which fully exploit the normal Hilbert module property of the time…
We are studying stationary random processes with conditional polynomial moments that allow a continuous path modification. Processes with continuous path modification, are important because they are relatively easy to simulate. One does not…
Modelling physical data with linear discrete time series, namely Fractionally Integrated Autoregressive Moving Average (ARFIMA), is a technique which achieved attention in recent years. However, these models are used mainly as a statistical…
The unicity of the time-varying quantile-based spectrum proposed in Birr et al. (2016) is established via an asymptotic representation result involving Wigner-Ville spectra.
In this paper we study the self-similar processes with stationary increments in a discrete-time setting. Different from the continuous-time case, it is shown that the scaling function of such a process may not take the form of a power…
Multivariate $\operatorname {COGARCH}(1,1)$ processes are introduced as a continuous-time models for multidimensional heteroskedastic observations. Our model is driven by a single multivariate L\'{e}vy process and the latent time-varying…
Following our previous work [68], this paper continues to investigate the evolution dynamics of local times of spectrally positive L\'evy processes with Gaussian components in the spatial direction. We prove that conditioned on the…
We study the non-stationary Feller process with time varying coefficients. We obtain the exact probability distribution exemplified by its characteristic function and cumulants. In some particular cases we exactly invert the distribution…
We consider the piecewise-deterministic Markov process obtained by randomly switching between the flows generated by a finite set of smooth vector fields on a compact set. We obtain H\"ormander-type conditions on the vector fields…
In this work, we consider simple systems that are influenced by Hamiltonians with time periodicity. Our analysis is mainly focussed on the density matrix approach and aims to solve the Liouville equation of motion from which one can extract…
LSST is expected to yield ~10^7 light curves over the course of its mission, which will require a concerted effort in automated classification. Stochastic processes provide one means of quantitatively describing variability with the…
We investigate the stationary states of one-dimensional driven diffusive systems, coupled to boundary reservoirs with fixed particle densities. We argue that the generic phase diagram is governed by an extremal principle for the macroscopic…
This paper describes a general investigation of stationary oscillations of galaxies. It begins with a linear analysis of modes of oscillation with continuous spectra of real frequencies. Such modes are gravitational analogues of the van…
We study the emergence of typicality in classical systems with a large number of binary state variables. We show analytically that for sufficiently large subsets of the complete state space, state functions which can be associated with…
Rate processes are simple and analytically tractable models for many dynamical systems which switch stochastically between a discrete set of quasi stationary states but they may also approximate continuous processes by coarse grained,…
We consider a L\'evy driven continuous time moving average process $X$ sampled at random times which follow a renewal structure independent of $X$. Asymptotic normality of the sample mean, the sample autocovariance, and the sample…
We study the local linear estimator for the drift coefficient of stochastic differential equations driven by $\alpha$-stable L\'{e}vy motions observed at discrete instants letting $T \rightarrow \infty$. Under regular conditions, we derive…
We develop a scale-invariant truncated L\'evy (STL) process to describe physical systems characterized by correlated stochastic variables. The STL process exhibits L\'evy stability for the probability density, and hence shows scaling…