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THE DIRECT-CONNECTEDNESS FUNCTION IN THE RANDOM CONNECTION MODEL

期刊: ADVANCES IN APPLIED PROBABILITY, 2023; 55 (1)

We investigate expansions for connectedness functions in the random connection model of continuum percolation in powers of the intensity. Precisely, w......

INTERACTING NONLINEAR REINFORCED STOCHASTIC PROCESSES: SYNCHRONIZATION OR NON-SYNCHRONIZATION

期刊: ADVANCES IN APPLIED PROBABILITY, 2023; 55 (1)

The rich-get-richer rule reinforces actions that have been frequently chosen in the past. What happens to the evolution of individuals' inclinations t......

LARGE-TIME BEHAVIOUR AND THE SECOND EIGENVALUE PROBLEM FOR FINITE-STATE MEAN-FIELD INTERACTING PARTICLE SYSTEMS

期刊: ADVANCES IN APPLIED PROBABILITY, 2023; 55 (1)

This article examines large-time behaviour of finite-state mean-field interacting particle systems. Our first main result is a sharp estimate (in the ......

CONSTRUCTION OF AGGREGATION PARADOXES THROUGH LOAD-SHARING MODELS

期刊: ADVANCES IN APPLIED PROBABILITY, 2023; 55 (1)

We show that load-sharing models (a very special class of multivariate probability models for nonnegative random variables) can be used to obtain basi......

LARGE-SCALE BEHAVIOR OF A PARTICLE SYSTEM WITH MEAN-FIELD INTERACTION: TRAVELING WAVE SOLUTIONS

期刊: ADVANCES IN APPLIED PROBABILITY, 2023; 55 (1)

We use probabilistic methods to study properties of mean-field models, which arise as large-scale limits of certain particle systems with mean-field i......

ON q-SCALE FUNCTIONS OF SPECTRALLY NEGATIVE LEVY PROCESSES

期刊: ADVANCES IN APPLIED PROBABILITY, 2023; 55 (1)

We obtain series expansions of the q-scale functions of arbitrary spectrally negative Levy processes, including processes with infinite jump activity,......

GRADIENT ESTIMATION FOR SMOOTH STOPPING CRITERIA

期刊: ADVANCES IN APPLIED PROBABILITY, 2023; 55 (1)

We establish sufficient conditions for differentiability of the expected cost collected over a discrete-time Markov chain until it enters a given set.......

A NEW MATRIX-INFINITE-PRODUCT-FORM SOLUTION FOR UPPER BLOCK-HESSENBERG MARKOV CHAINS AND ITS QUASI-ALGORITHMIC CONSTRUCTIBILITY

期刊: ADVANCES IN APPLIED PROBABILITY, 2023; 55 (1)

This paper presents a new matrix-infinite-product-form (MIP-form) solution for the stationary distribution in upper block-Hessenberg Markov chains (UB......

OPTIMAL MULTIPLE STOPPING PROBLEM UNDER NONLINEAR EXPECTATION

期刊: ADVANCES IN APPLIED PROBABILITY, 2023; 55 (1)

In this paper, we study the optimal multiple stopping problem under the filtration-consistent nonlinear expectations. The reward is given by a set of ......

FULL CLASSIFICATION OF DYNAMICS FOR ONE-DIMENSIONAL CONTINUOUS-TIME MARKOV CHAINS WITH POLYNOMIAL TRANSITION RATES

期刊: ADVANCES IN APPLIED PROBABILITY, 2023; 55 (1)

This paper provides a full classification of the dynamics for continuous-time Markov chains (CTMCs) on the nonnegative integers with polynomial transi......

MATRIX CALCULATIONS FOR MOMENTS OF MARKOV PROCESSES

期刊: ADVANCES IN APPLIED PROBABILITY, 2023; 55 (1)

Matryoshka dolls, the traditional Russian nesting figurines, are known worldwide for each doll's encapsulation of a sequence of smaller dolls. In this......

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