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We present distributions of countable models and correspondent structural characteristics of complete theories with continuum many types: for prime models over finite sets relative to Rudin-Keisler preorders, for limit models over types and…
For noncorrelated random variables, we study a concentration property of the family of distributions of normalized sums formed by sequences of times of a given large length.
A defining feature of non-stationary systems is the time dependence of their statistical parameters. Measured time series may exhibit Gaussian statistics on short time horizons, due to the central limit theorem. The sample statistics for…
We determine the asymptotic distribution of the sum of correlated variables described by a matrix product ansatz with finite matrices, considering variables with finite variances. In cases when the correlation length is finite, the law of…
Superslow diffusion, i.e., the long-time diffusion of particles whose mean-square displacement (variance) grows slower than any power of time, is studied in the framework of the decoupled continuous-time random walk model. We show that this…
A single queueing system with time-dependent exponentially distributed arrival processes and exponential machine processes (Kendall notation $M_t/M_t/1$) is analyzed. Modeling the time evolution for the discrete queue-length distribution by…
In the paper, multivariate probability distributions are considered that are representable as scale mixtures of multivariate elliptically contoured stable distributions. It is demonstrated that these distributions form a special subclass of…
We study the properties of a subclass of stochastic processes called discrete time nonlinear Markov chains with an aggregator, which naturally appear in various topics such as strategic queueing systems, inventory dynamics, opinion…
We introduce and study a multiparameter version of the generalized counting process (GCP), where there is a possibility of finitely many arrivals simultaneously. We call it the multiparameter GCP. In a particular case, it is uniquely…
We are concerned with the general problem of proving the existence of joint distributions of two discrete random variables $M$ and $N$ subject to infinitely many constraints of the form $\mathbb{P}\left(M=i,N=j\right)=0$. In particular, the…
The paper deals with a certain class of random evolutions. We develop a construction that yields an invariant measure for a continuous-time Markov process with random transitions. The approach is based on a particular way of constructing…
A new family of multivariate distributions, which shall be termed multivector variate distributions, based in the family of the multivariate contoured elliptically distribution is proposed. Several particular cases of multivector variate…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…
We revisit the problem of condensation for independent, identically distributed random variables with a power-law tail, conditioned by the value of their sum. For large values of the sum, and for a large number of summands, a condensation…
Multivariate probability density functions of returns are constructed in order to model the empirical behavior of returns in a financial time series. They describe the well-established deviations from the Gaussian random walk, such as an…
Let $T\$ be a stopping time associated with a sequence of independent random variables $Z_{1},Z_{2},...$ . By applying a suitable change in the probability measure we present relations between the moment or probability generating functions…
In this paper we propose a family of multivariate asymmetric distributions over an arbitrary subset of set of real numbers which is defined in terms of the well-known elliptically symmetric distributions. We explore essential properties,…
We extend the synthetic theories of discrete and Gaussian categorical probability by introducing a diagrammatic calculus for reasoning about hybrid probabilistic models in which continuous random variables, conditioned on discrete ones,…
Moments of secular and inverse secular coefficients, averaged over random matrices from classical groups, are related to the enumeration of non-negative matrices with prescribed row and column sums. Similar random matrix averages are…
The paper investigates the problem of performing correlation analysis when the number of observations is very large. In such a case, it is often necessary to combine the random observations to achieve dimensionality reduction of the…