Related papers: Some martingale characterizations of compound mixe…
We establish necessary and sufficient conditions implying that the product of $m\geq 2$ Poisson functionals, living in a finite sum of Wiener chaoses, is square-integrable. Our conditions are expressed in terms of iterated add-one cost…
We prove what appears to be the first concentration of measure result for hidden Markov processes. Our bound is stated in terms of the contraction coefficients of the underlying Markov process, and strictly generalizes the Markov process…
We develop a prior probability model for temporal Poisson process intensities through structured mixtures of Erlang densities with common scale parameter, mixing on the integer shape parameters. The mixture weights are constructed through…
We use orthogonality measures of Askey--Wilson polynomials to construct Markov processes with linear regressions and quadratic conditional variances. Askey--Wilson polynomials are orthogonal martingale polynomials for these processes.
In the present paper we demonstrate the results of a statistical analysis of some characteristics of precipitation events and propose a kind of a theoretical explanation of the proposed models in terms of mixed Poisson and mixed exponential…
Extreme values are considered in samples with random size that has a mixed Poisson distribution being generated by a doubly stochastic Poisson process. We prove some inequalities providing bounds on the rate of convergence in limit theorems…
For a general renewal process $N$ (allowing delay, defect and multiple simultaneous arrivals) the independence of the first renewal epochs of the marked processes got from $N$ by Bernoulli $0$/$1$ thinning is characterized. This…
We herein review the recent progress on the study of metastability based on the analysis of solutions of Poisson equations related to the generators of the underlying metastable dynamics. This review paper is based on the joint work with…
In this article, we derive the state probabilities of different type of space- and time-fractional Poisson processes using z-transform. We work on tempered versions of time-fractional Poisson process and space-fractional Poisson processes.…
I present here a simple proof that, under general regularity conditions, the standard parametrization of generalized linear mixed model is identifiable. The proof is based on the assumptions of generalized linear mixed models on the first…
This note investigates core properties of martingales, emphasizing the measure-theoretic formulation of conditional expectation, the martingale transform, and the upcrossing lemma. These results lead to the Martingale Convergence Theorem,…
Marked point process data arise when events occur in a space with event-level marks. We study clustering of replicated marked Poisson point processes and introduce Dirichlet process mixtures of marked Poisson point processes, a Bayesian…
We prove a multidimensional Poisson limit theorem in free probability, and define joint free Poisson distributions in a non-commutative probability space. We define (compound) free Poisson process explicitly, similar to the definitions of…
In this paper we survey and further study partial sums of a stationary process via approximation with a martingale with stationary differences. Such an approximation is useful for transferring from the martingale to the original process the…
This paper deals with the question of conditional sampling and prediction for the class of stationary max-stable processes which allow for a mixed moving maxima representation. We develop an exact procedure for conditional sampling using…
[Takayasu et al., Phys. Rev.Lett. 79, 966 (1997)] revisited the question of stochastic processes with multiplicative noise, which have been studied in several different contexts over the past decades. We focus on the regime, found for a…
We investigate aspects of semimartingale decompositions, approximation and the martingale representation for multidimensional correlated Markov processes. A new interpretation of the dependence among processes is given using the martingale…
We prove a Poisson process approximation result for stabilizing functionals of a determinantal point process. Our results use concrete couplings of determinantal processes with different Palm measures and exploit their association…
Strictly stationary INAR(1) ("integer-valued autoregressive processes of order 1") with Poisson innovations are "interlaced rho-mixing".
We study point processes that consist of certain centers of point tuples of an underlying Poisson process. Such processes arise in stochastic geometry in the study of exceedances of various functionals describing geometric properties of the…