Related papers: Multifractional Poisson process, multistable subor…
Multifractal scaling has been extensively studied for real-valued stochastic processes, but a systematic integer-valued analogue has remained largely unexplored. In this work, we introduce a multifractal framework for integer-valued…
We consider a weighted sum of a series of independent Poisson random variables and show that it results in a new compound Poisson distribution which includes the Poisson distribution and Poisson distribution of order k. An explicit…
The linear fractional stable motion generalizes two prominent classes of stochastic processes, namely stable L\'evy processes, and fractional Brownian motion. For this reason it may be regarded as a basic building block for continuous time…
We consider a fractional counting process with jumps of amplitude $1,2,\ldots,k$, with $k\in \mathbb{N}$, whose probabilities satisfy a suitable system of fractional difference-differential equations. We obtain the moment generating…
A multivariate, stationary time series is said to be jointly regularly varying if all its finite-dimensional distributions are multivariate regularly varying. This property is shown to be equivalent to weak convergence of the conditional…
We define a large class of multifractal random measures and processes with arbitrary log-infinitely divisible exact or asymptotic scaling law. These processes generalize within a unified framework both the recently defined log-normal…
We define and study the multiparameter fractional Brownian motion. This process is a generalization of both the classical fractional Brownian motion and the multiparameter Brownian motion, when the condition of independence is relaxed.…
What constitutes jointly Poisson processes remains an unresolved issue. This report reviews the current state of the theory and indicates how the accepted but unproven model equals that resulting from the small time-interval limit of…
We present new properties for the Fractional Poisson process and the Fractional Poisson field on the plane. A martingale characterization for Fractional Poisson processes is given. We extend this result to Fractional Poisson fields,…
In the paper we present the governing equations for marginal distributions of Poisson and Skellam processes time-changed by inverse subordinators. The equations are given in terms of convolution-type derivatives.
Subordinators are infinitely divisible distributions on the positive half-line. They are often used as mixing distributions in Poisson mixtures. We show that appropriately scaled Poisson mixtures can approximate the mixing subordinator and…
In this paper, we introduce and study fractional versions of three compound Poisson processes, namely, the Bell-Touchard process, the Poisson-logarithmic process and the generalized P\'olya-Aeppli process. It is shown that these processes…
We prove large deviation principles for two versions of fractional Poisson processes. Firstly we consider the main version which is a renewal process; we also present large deviation estimates for the ruin probabilities of an insurance…
This paper considers a simulation-based estimator for a general class of Markovian processes and explores some strong consistency properties of the estimator. The estimation problem is defined over a continuum of invariant distributions…
We develop a practical approach to establish the stability, that is, the recurrence in a given set, of a large class of controlled Markov chains. These processes arise in various areas of applied science and encompass important numerical…
In this note we generalise the Phillips theorem on the subordination of Feller processes by Levy subordinators to the class of additive subordinators (i.e. subordinators with independent but possibly nonstationary increments). In the case…
We consider the fully-coupled McKean-Vlasov equation with multi-time-scale potentials, and all the coefficients depend on the distributions of both the slow component and the fast motion. By studying the smoothness of the solution of the…
In this paper, we introduce a bivariate tempered space-fractional Poisson process (BTSFPP) by time-changing the bivariate Poisson process with an independent tempered $\alpha$-stable subordinator. We study its distributional properties and…
The study of non-stationary processes whose local form has controlled properties is a fruitful and important area of research, both in theory and applications. We present here a construction of multifractional multistable processes, based…
The reduction of a continuous Markov process with multiple metastable states to a discrete rate process is investigated in the presence of slow time dependent parameters such as periodic external forces or slowly fluctuating barrier…