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Moving from univariate to bivariate jointly dependent long-memory time series introduces a phase parameter $(\gamma)$, at the frequency of principal interest, zero; for short-memory series $\gamma=0$ automatically. The latter case has also…
By the methods of multitype branching processes in random environment counted by random characteristics we study the tail distribution of busy periods and some other characteristics of the branching type polling systems in which the service…
We introduce a new general concept of surrogate random variable, the ``surrogate by exchangeability'' that allows to study the class of random variables that can be decomposed by means of an independent randomisation. As an example, we…
The purpose of this article is to introduce a new L\'evy process, termed Variance Gamma++ process, to model the dynamic of assets in illiquid markets. Such a process has the mathematical tractability of the Variance Gamma process and is…
Invariant sets define regions of the state space where system constraints are always satisfied. The majority of numerical techniques for computing invariant sets have been developed for discrete-time systems with a fixed sampling time.…
Consider a list of labeled objects that are organized in a heap. At each time, object $j$ is selected with probability $p_j$ and moved to the top of the heap. This procedure defines a Markov chain on the set of permutations which is…
We provide some equations for the Variance Gamma process due to the fact that we do not consider only the definition as a time-changed Brownian motion. This brings us to a new non-local equation, even true in the drifted case, involving…
This paper focuses on studying the long-time dynamics of the subordination process for a range of linear evolution equations, with a special emphasis on the fractional heat equation. By treating inverse subordinators as random time…
We introduce a generalized Bayesian method for multiple changepoint analysis with a loss function inspired by multinomial logistic regression. The method does not require a specification of the data-generating process and avoids restrictive…
Rules for the transformation of time parameters in relativistic Langevin equations are derived and discussed. In particular, it is shown that, if a coordinate-time parameterized process approaches the relativistic Juttner-Maxwell…
We consider component-wise equivariant estimation of order restricted location/scale parameters of a general bivariate distribution under quite general conditions on underlying distributions and the loss function. This paper unifies various…
For $\widetilde{\cal R} = 1 - \exp(- {\cal R})$ a random closed set obtained by exponential transformation of the closed range ${\cal R}$ of a subordinator, a regenerative composition of generic positive integer $n$ is defined by recording…
Consider a multivariate L\'evy-driven Ornstein-Uhlenbeck process where the stationary distribution or background driving L\'evy process is from a parametric family. We derive the likelihood function assuming that the innovation term is…
In this paper, we analyze a L{\'e}vy model based on two popular concepts - subordination and L{\'e}vy copulas. More precisely, we consider a two-dimensional L{\'e}vy process such that each component is a time-changed (subordinated) Brownian…
We study positive random variables whose moments can be expressed by products and quotients of Gamma functions; this includes many standard distributions. General results are given on existence, series expansion and asymptotics of density…
We study the asymptotic behaviour of the time-changed stochastic process $\vphantom{X}^f\!X(t)=B(\vphantom{S}^f\!S (t))$, where $B$ is a standard one-dimensional Brownian motion and $\vphantom{S}^f\!S$ is the (generalized) inverse of a…
Let $\{D(s), s \geq 0\}$ be a non-decreasing L\'evy process. The first-hitting time process $\{E(t) t \geq 0\}$ (which is sometimes referred to as an inverse subordinator) defined by $E(t) = \inf \{s: D(s) > t \}$ is a process which has…
We define generalized innovations associated with generalized error models having arbitrary distributions, that is, distributions that can be mixtures of continuous and discrete distributions. These models include stochastic volatility…
We propose a flexible model for count time series which has potential uses for both underdispersed and overdispersed data. The model is based on the Conway-Maxwell-Poisson (COM-Poisson) distribution with parameters varying along time to…
In this article, we introduce the mean independent component analysis for multivariate time series to reduce the parameter space. In particular, we seek for a contemporaneous linear transformation that detects univariate mean independent…