Related papers: Subordinated Compound Poisson processes of order $…
Let $\tilde{N}\_{t}$ be a standard compensated Poisson process on $[0,1]$. We prove a new characterization of anticipating integrals of the Skorohod type with respect to $\tilde{N}$, and use it to obtain several counterparts to well…
In this paper we study the complex symmetry in the several variable Fock space by using the techniques of weighted composition operators and semigroups. We characterize unbounded weighted composition operators that are (real) complex…
Nonequilibrium behaviors of positional order are discussed based on diffusion processes in particle systems. With the cumulant expansion method up to the second order, we obtain a relation between the positional order parameter $\Psi$ and…
A number of numeric approaches to simulate Poisson point processes with arbitrary event rates are presented and implemented for R. They include the simulation of the number of points and their location as well as the determination of…
Random events in space and time often exhibit a locally dependent structure. When the events are very rare and dependent structure is not too complicated, various studies in the literature have shown that Poisson and compound Poisson…
To analyse interaction in marked spatio-temporal point processes (MSTPPs), we introduce marked (cross) second-order reduced moment measures and K-functions for general inhomogeneous second-order intensity reweighted stationary MSTPPs. These…
A framework to systematically decouple high order elliptic equations into combination of Poisson-type and Stokes-type equations is developed. The key is to systematically construct the underling commutative diagrams involving the complexes…
A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…
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…
Real count data time series often show the phenomenon of the underdispersion and overdispersion. In this paper, we develop two extensions of the first-order integer-valued autoregressive process with Poisson innovations, based on binomial…
We introduce decomposition complexes of posets, which generalize order complexes. The main advantage of our construction is that decomposition complexes are closed under taking products. Other special instances of this theory include nested…
Weakly stationary random processes of $k$-dimensional affine subspaces (flats) in $\mathbb{R}^n$ are considered. If $2k\geq n$, then intersection processes are investigated, while in the complementary case $2k<n$ a proximity process is…
The electronic phase diagrams of many highly correlated systems, and in particular the cuprate high temperature superconductors, are complex, with many different phases appearing with similar-sometimes identical-ordering temperatures even…
We present an orthogonal matrix outer product decomposition for the fourth-order conjugate partial-symmetric (CPS) tensor and show that the greedy successive rank-one approximation (SROA) algorithm can recover this decomposition exactly.…
In this paper introduces a new family of continuous distributions namely the Poison transmuted-G family of distribution is proposed by inducing two addition parameter on the base line G distribution. Some of its mathematical properties…
We study a family of Markov processes on $\mathcal{P}^{(k)}$, the space of partitions of the natural numbers with at most $k$ blocks. The process can be constructed from a Poisson point process on…
Local superlinear convergence of the semismooth Newton method usually necessitates assumptions on the uniform invertibility of the utilized, generalized Jacobian matrices, such as, e.g., BD- or CD-regularity. For certain composite-type…
An expository summary of properties of the poset of Dyck paths ordered by inclusion.
We present a satisfactory definition of the important class of L\'evy processes indexed by a general collection of sets. We use a new definition for increment stationarity of set-indexed processes to obtain different characterizations of…
In this paper, we study a discrete-time analogue of a Hawkes process, modelled as a Poisson autoregressive process whose parameters depend on the past of the trajectory. The model is characterized to allow these parameters to take negative…