Related papers: On $q$-scale functions of spectrally negative comp…

We present a general class of spatio-temporal stochastic processes describing the causal evolution of a positive-valued field in space and time. The field construction is based on independently scattered random measures of Levy type whose…

We consider a Markov process on non-negative integer arrays of a certain shape, this shape being determined by general parameters in the model which correspond to drifts. In the case where these drifts are trivial, the arrays are reverse…

A functional representation of free L\'evy processes is established via an ensemble of unitarily invariant Hermitian matrix-valued L\'evy processes. This is accomplished by proving functional asymptotics of their empirical spectral…

Motivated by potential applications to partial differential equations, we develop a theory of fine scales of decay rates for operator semigroups. The theory contains, unifies, and extends several notable results in the literature on decay…

In this paper we present multivariate space-time fractional Poisson processes by considering common random time-changes of a (finite-dimensional) vector of independent classical (non-fractional) Poisson processes. In some cases we also…

This paper introduces a generalization of the so-called space-fractional Poisson process by extending the difference operator acting on state space present in the associated difference-differential equations to a much more general form. It…

The evolution of scalar fields transported by turbulent flow is characterized by the presence of fronts, which rule the small-scale statistics of scalar fluctuations. With the aid of numerical simulations, it is shown that: isotropy is not…

The first passage time process of a L\'evy subordinator with heavy-tailed L\'evy measure has long-range dependent paths. The random fluctuations that appear under two natural schemes of summation and time scaling of such stochastic…

We derive a generalized version of the work fluctuation theorem for nonequilibrium systems with spatio-temporal temperature fluctuations. For chi-square distributed inverse temperature we obtain a generalized fluctuation theorem based on…

The observation of scaling in processes in which a weakly interacting probe delivers large momentum ${\bf q}$ to a many-body system simply reflects the dominance of incoherent scattering off target constituents. While a suitably defined…

Strong negative dependence properties have recently been proved for the symmetric exclusion process. In this paper, we apply these results to prove convergence to the Poisson and normal distributions for various functionals of the process.

In this write-up, I summarize the analyses on the low-lying scalar mesons I have done recently with my collaborators. I first briefly review the previous analyses on the hadronic processes related to the scalar mesons, which shows that the…

In this paper, we solve exit problems for a level-dependent L\'evy process which is exponentially killed with a killing intensity that depends on the present state of the process. Moreover, we analyse the respective resolvents. All…

The pion structure function is investigated in a simple model, where pion and constituent quark fields are coupled through the simplest pseudoscalar coupling. The imaginary part of the forward gamma* pi-> gamma* pi scattering amplitude is…

The quantum Brownian motion of a charged particle in the electromagnetic vacuum fluctuations is investigated near a perfectly reflecting flat boundary, taking into account the smooth switching process in the measurement. Constructing a…

In this paper, we obtain some Simpson type inequalities for functions whose second derivatives absolute value or q-th power of them are Q-class functions. Also we give applications to numerical integration.

We construct a general stochastic process and prove weak convergence results. It is scaled in space and through the parameters of its distribution. We show that our simplified scaling is equivalent to time scaling used frequently. The…

Fractional generalizations of the Poisson process and branching Furry process are considered. The link between characteristics of the processes, fractional differential equations and Levy stable densities are discussed and used for…

There is an abundance of useful fluctuation identities for one-sided L\'evy processes observed up to an independent exponentially distributed time horizon. We show that all the fundamental formulas generalize to time horizons having matrix…

The concepts of scale invariance, self-similarity and scaling have been fruitfully applied to the study of price fluctuations in financial markets. After a brief review of the properties of stable Levy distributions and their applications…