Related papers: On additive time-changes of Feller processes
We study the three-dimensional Navier-Stokes equations in a periodic domain with the force decaying in time. Although the force has a certain coherent decay, as time tends to infinity, it can be too complicated for the previous theory of…
Let $\mathbb{R}^N_+= [0,\infty)^N$. We here consider a class of random fields $(X_t)_{t\in \mathbb{R}^N_+}$ which are known as Multiparameter L\'evy processes. Related multiparameter semigroups of operators and their generators are…
We establish a novel characterisation of the law of the convex minorant of any L\'evy process. Our self-contained elementary proof is based on the analysis of piecewise linear convex functions and requires only very basic properties of…
We are interested in the rate of convergence of a subordinate Markov process to its invariant measure. Given a subordinator and the corresponding Bernstein function (Laplace exponent) we characterize the convergence rate of the subordinate…
In this work we study the solutions to some fractional higher-order equations. Special cases in which time-fractional derivatives take integer values are also examined and the explicit solutions are presented. Such solutions can be…
In our previous paper (ArXiv:1306.1492) we have proved that a representation of the infinitesimal generators $L$ for Levy processes $X_t$ can be written down in a convolution type form. For the case of non-summable Levy measures we…
We present and demonstrate a version of Levinson's theorem especially dedicated to the asymptotic behavior of form factor phases. Indeed, as required by analyticity, form factors are multi-valued complex functions of a square four-momentum…
Many forms of dependence manifest themselves over time, with behavior of variables in dynamical systems as a paradigmatic example. This paper studies temporal dependence in dynamical systems from a logical perspective, by enriching a…
The theory of monotonicity and duality is developed for general one-dimensional Feller processes. Moreover it is shown that local monotonicity conditions (conditions on the L\'evy kernel) are sufficient to prove the well-posedness of the…
This paper studies theory and inference related to a class of time series models that incorporates nonlinear dynamics. It is assumed that the observations follow a one-parameter exponential family of distributions given an accompanying…
In this article, we introduce Skellam process of order k and its running average. We also discuss the time-changed Skellam process of order k. In particular we discuss space-fractional Skellam process and tempered space-fractional Skellam…
Various recent results on quantum L\'evy processes are presented. The first part provides an introduction to the theory of L\'evy processes on involutive bialgebras. The notion of independence used for these processes is tensor…
We study a real-valued L\'evy-type process $X$, which is locally $\alpha$-stable in the sense that its jump kernel is a combination of a `principal' (state dependent) $\alpha$-stable part with a `residual' lower order part. We show that…
We completely describe the size and large intersection properties of the Holder singularity sets of Levy processes. We also study the set of times at which a given function cannot be a modulus of continuity of a Levy process. The Holder…
A time and space inhomogeneous Markov process is a Feller evolution process, if the corresponding evolution system on the continuous functions vanishing at infinity is strongly continuous. We discuss generators of such systems and show that…
We consider time-changed Poisson processes, and derive the governing difference-differential equations (DDE) these processes. In particular, we consider the time-changed Poisson processes where the the time-change is inverse Gaussian, or…
These lecture notes concern the basics of the theory of process behaviour. First the concept of a (labelled) transition system receives ample treatment and then the following issues concerning process behaviour are elaborated in the setting…
In this paper, we study the existence and uniqueness of solutions for general fractional-time parabolic equations of mixture type, and their probabilistic representations in terms of the corresponding inverse subordinators with or without…
We study the asymptotic behaviour of a properly normalized time-changed multidimensional Wiener process; the time change is given by an additive functional of the Wiener process itself. At the level of generators, the time change means that…
In this paper, we study a multivariate version of the generalized counting process (GCP) and discuss its various time-changed variants. The time is changed using random processes such as the stable subordinator, inverse stable subordinator,…