Related papers: Tempered relaxation equation and related generaliz…
Necessary and sufficient conditions are presented for the existence of (second order) stationary solutions of the generalized Langevin equation under appropriate assumptions on the associated memory kernel. When this stochastic equation is…
Reaction-diffusion equations coupled to ordinary differential equations (ODEs) may exhibit spatially low-regular stationary solutions. This work provides a comprehensive theory of asymptotic stability of bounded, discontinuous or…
Discrete stability extends the classical notion of stability to random elements in discrete spaces by defining a scaling operation in a randomised way: an integer is transformed into the corresponding binomial distribution. Similarly…
In the present paper, we address a class of the fractional derivatives of constant and variable orders for the first time. Fractional-order relaxation equations of constants and variable orders in the sense of Caputo type are modeled from…
We investigate the notion of finite time stability for tempered fractional systems (TFSs) with time delays and variable coefficients. Then, we examine some sufficient conditions that allow concluding the TFSs stability in a finite time…
Dielectric measurements on molecular liquids just above the glass transition indicate that alpha relaxation is characterized by a generic high-frequency loss varying as $\omega^{-1/2}$, whereas deviations from this come from one or more…
We propose a moving mesh adaptive approach for solving time-dependent partial differential equations. The motion of spatial grid points is governed by a moving mesh PDE (MMPDE) in which a mesh relaxation time \tau is employed as a…
Studying sample path behaviour of stochastic fields/processes is a classical research topic in probability theory and related areas such as fractal geometry. To this end, many methods have been developed since a long time in Gaussian…
This paper is a preliminary work to address the problem of dynamical systems with parameters varying in time. An idea to predict their behaviour is proposed. These systems are called \emph{transient systems}, and are distinguished from…
We develop the first exact and computationally tractable method for simulating from tempered stable distributions in the infinite variation case, which corresponds to $\alpha\in[1,2)$. A small simulation study shows that the approach works…
A statistical algorithm for estimating the characteristic parameter $\alpha$ of the stable law is presented and the estimate of its quadratic deviation is obtained in the paper. This algorithm is applied in the description of the…
The presence of fluctuating local relaxation times, $\tau_r(t)$ has been used for some time as a conceptual tool to describe dynamical heterogeneities in glass-forming systems. However, until now no general method is known to extract the…
We explore the well-posedness of the fractional version of Zener's wave equation for viscoelastic solids, which is based on a constitutive law relating the stress tensor $\boldsymbol{\sigma}$ to the strain tensor $\boldsymbol\varepsilon(\bf…
We study the process of relaxation back to thermal equilibrium in $(1+1)$-dimensional conformal field theory at finite temperature. When the size of the system is much larger than the inverse temperature, perturbations decay exponentially…
The reactive process of barrier escaping from the metastable potential well is studied together with the extension of Kramers' rate formula to the fractional case. Characteristic quantities are computed for an thimbleful of insight into the…
We identify the stochastic processes associated with one-sided fractional partial differential equations on a bounded domain with various boundary conditions. This is essential for modelling using spatial fractional derivatives. We show…
A time-varying empirical spectral process indexed by classes of functions is defined for locally stationary time series. We derive weak convergence in a function space, and prove a maximal exponential inequality and a…
We consider the time-varying actuator placement in continuous time, where the goal is to maximize the trace of the controllability Grammian. A natural relaxation of the problem is to allow the binary $\{0,1\}$ variable indicating whether an…
Linear fractional Galton-Watson branching processes in i.i.d.~random environment are, on the quenched level, intimately connected to random difference equations by the evolution of the random parameters of their linear fractional marginals.…
We describe a new class of self-similar symmetric $\alpha$-stable processes with stationary increments arising as a large time scale limit in a situation where many users are earning random rewards or incurring random costs. The resulting…