Related papers: On total claim amount for marked Poisson cluster m…
We present a mixture Poisson model for claims counts in which the number of components in the mixture are estimated by reversible jump MCMC methods.
This paper studies the properties of the Multiply Iterated Poisson Process (MIPP), a stochastic process constructed by repeatedly time-changing a Poisson process, and its applications in ruin theory. Like standard Poisson processes, MIPPs…
The Markov-modulated Poisson process is utilised for count modelling in a variety of areas such as queueing, reliability, network and insurance claims analysis. In this paper, we extend the Markov-modulated Poisson process framework through…
We obtain a Poisson Limit for return times to small sets for product systems. Only one factor is required to be hyperbolic while the second factor is only required to satisfy polynomial deviation bounds for ergodic sums. In particular, the…
The results in this paper provide new information on asymptotic properties of classical models: the neutral Kingman coalescent under a general finite-alleles, parent-dependent mutation mechanism, and its generalisation, the ancestral…
The generalized Poisson distribution is well known to be a compound Poisson distribution with Borel summands. As a generalization we present closed formulas for compound Bartlett and Delaporte distributions with Borel summands and a…
We investigate random partitions of complete graphs defined by Poissonian emsembles of Markov loops
This paper studies the joint moments of a compound discounted renewal process observed at different times with each arrival removed from the system after a random delay. This process can be used to describe the aggregate (discounted)…
Consider two insurance companies (or two branches of the same company) that divide between them both claims and premia in some specified proportions. We model the occurrence of claims according to a renewal process. One ruin problem…
We study randomly stopped sums via their asymptotic scales. First, finiteness of moments is considered. To generalise this study, asymptotic scales applicable to the class of all heavy-tailed random variables are used. The stopping is…
We study expectation values of matrix elements for boundary values of the resolvent as well as the density of states for a random Schr\"odinger operator with potential distributed according to a Poisson process. Asymptotic expansions for…
We have established a sparse estimation method for the generalized exponential marked Hawkes process by the penalized method to the ordinary method (P-O) estimator. Furthermore, we evaluated the probability of correct variable selection. In…
This paper establishes asymptotic results for the maximum likelihood and restricted maximum likelihood (REML) estimators of the parameters in the nested error regression model for clustered data when both of the number of independent…
Hayes equivalence is defined on monic polynomials over a finite field $\fq$ in terms of the prescribed leading coefficients and the residue classes modulo a given monic polynomial $Q$. We study the distribution of the number of zeros in a…
In this paper, we prove a conditional limit theorem for independent not necessarily identically distributed random variables. Namely, we obtain the asymptotic distribution of a large number of them given the sum.
A validated simulation model primarily requires performing an appropriate input analysis mainly by determining the behavior of real-world processes using probability distributions. In many practical cases, probability distributions of the…
We study local normal forms for completely integrable systems on Poisson manifolds in the presence of additional symmetries. The symmetries that we consider are encoded in actions of compact Lie groups. The existence of Weinstein's…
This paper deals with the union set of a stationary Poisson process of cylinders in $\mathbb{R}^n$ having an $(n-m)$-dimensional base and an $m$-dimensional direction space, where $m\in\{0,1,\ldots,n-1\}$ and $n\geq 2$. The concept…
We propose an aproach for asymptotic analysis of plane partition statistics related to counts of parts whose sizes exceed a certain suitably chosen level. In our study, we use the concept of conjugate trace of a plane partition of the…
In this paper, we revisit the classical results on the generalized St. Petersburg sums. We determine the limit distribution of the St. Petersburg sum conditioning on its maximum, and we analyze how the limit depends on the value of the…