Related papers: On additive time-changes of Feller processes

In the last years, many authors studied a class of continuous time semi-Markov processes obtained by time-changing Markov processes by hitting times of independent subordinators. Such processes are governed by integro-differential…

In this work, with the help of fractional calculus, it is shown a time dependence of entropy more general than the well known Pesin relation is derived. Here the equiprobability postulate is not assumed, the system dynamic in the phase…

We extend the idea of tempering stable Levy processes to tempering more general classes of Levy processes. We show that the original process can be decomposed into the sum of the tempered process and an independent point process of large…

This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized…

Under an appropriate regular variation condition, the affinely normalized partial sums of a sequence of independent and identically distributed random variables converges weakly to a non-Gaussian stable random variable. A functional version…

Differentiation is an important task in control, observation and fault detection. Levant's differentiator is unique, since it is able to estimate exactly and robustly the derivatives of a signal with a bounded high-order derivative.…

We consider the large deviations associated with the empirical mean of independent and identically distributed random variables under a subexponential moment condition. We show that non-trivial deviations are observable at a subexponential…

We introduce and study renewal processes defined by means of extensions of the standard relaxation equation through ``stretched" non-local operators (of order $\alpha$ and with parameter $\gamma$). In a first case we obtain a generalization…

Let $X=\{X_{t},t\in R_{+}\}$ be a symmetric L\'evy process with local time $\{L^{x}_{t} ; (x,t)\in R^{1}\times R^{1}_{+}\}$. When the L\'evy exponent $\psi(\la)$ is regularly varying at infinity with index $1<\beta\leq 2$ and satisfies some…

The simple L\'evy Poisson process and scaled forms are explicitly constructed from partial sums of independent and identically distributed random variables and from sums of non-stationary independent random variables. For the latter, the…

We consider general convolutional derivatives and related fractional statistical dynamics of continuous interacting particle systems. We apply the subordination principle to construct kinetic fractional statistical dynamics in the continuum…

We construct $P(phi)_1$-processes indexed by the full time-line, separately derived from the functional integral representations of the relativistic and non-relativistic Nelson models in quantum field theory. These two cases differ…

We consider a Markov additive process with a finite phase space and study its path decompositions at the times of extrema, first passage and last exit. For these three families of times we establish splitting conditional on the phase, and…

We give a short introduction to the theory of L\'evy processes on dual groups. As examples we consider L\'evy processes with additive increments and L\'evy processes on the dual affine group.

We introduce supCARMA processes, defined as superpositions of L\'evy-driven CARMA processes with respect to a L\'evy basis, as a natural extension of the superpositions of Ornstein-Uhlenbeck type processes. We then focus on supCAR$(2)$…

We consider additive functionals of Markov processes in continuous time with general (metric) state spaces. We derive concentration bounds for their exponential moments and moments of finite order. Applications include diffusions,…

A branching L\'evy process can be seen as the continuous-time version of a branching random walk. It describes a particle system on the real line in which particles move and reproduce independently in a Poissonian manner. Just as for L\'evy…

The Friedrichs extension of minimal linear relation being bounded below and associated with the discrete symplectic system with a special linear dependence on the spectral parameter is characterized by using recessive solutions. This…

Long-time limit of one-dimensional L\'{e}vy processes weighted and normalized with respect to the exponential functional of two-point local times are studied. The limit processes may vary according to the choice of random clocks.

In this article, we introduce mixtures of tempered stable subordinators (TSS). These mixtures define a class of subordinators which generalize tempered stable subordinators. The main properties like probability density function (pdf), Levy…