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Random coefficients bifurcating autoregressive processes

Benoîte de Saporta, Anne Gégout-Petit, Laurence Marsalle (2014)

ESAIM: Probability and Statistics

This paper presents a new model of asymmetric bifurcating autoregressive process with random coefficients. We couple this model with a Galton−Watson tree to take into account possibly missing observations. We propose least-squares estimators for the various parameters of the model and prove their consistency, with a convergence rate, and asymptotic normality. We use both the bifurcating Markov chain and martingale approaches and derive new results in both these frameworks.

Regular behavior at infinity of stationary measures of stochastic recursion on NA groups

Dariusz Buraczewski, Ewa Damek (2010)

Colloquium Mathematicae

Let N be a simply connected nilpotent Lie group and let S = N ⋊ ( ℝ ⁺ ) d be a semidirect product, ( ℝ ⁺ ) d acting on N by diagonal automorphisms. Let (Qₙ,Mₙ) be a sequence of i.i.d. random variables with values in S. Under natural conditions, including contractivity in the mean, there is a unique stationary measure ν on N for the Markov process Xₙ = MₙXn-1 + Qₙ. We prove that for an appropriate homogeneous norm on N there is χ₀ such that l i m t → ∞ t χ ₀ ν x : | x | > t = C > 0 . In particular, this applies to classical Poisson kernels on symmetric spaces,...

Remarks on the boolean convolution and Kerov's α-transformation

Anna Dorota Krystek (2006)

Banach Center Publications

This paper consists of two parts. The first part is devoted to the study of continuous diagrams and their connections with the boolean convolution. In the second part we investigate the rectangular Young diagrams and respective discrete measures. We recall the definition of Kerov's α-transformation of diagrams, define the α-transformation of finitely supported discrete measures and generalize the notion of the α-transformation.

Renewal Processes of Mittag-Leffler and Wright Type

Mainardi, Francesco, Gorenflo, Rudolf, Vivoli, Alessandro (2005)

Fractional Calculus and Applied Analysis

2000 MSC: 26A33, 33E12, 33E20, 44A10, 44A35, 60G50, 60J05, 60K05.After sketching the basic principles of renewal theory we discuss the classical Poisson process and offer two other processes, namely the renewal process of Mittag-Leffler type and the renewal process of Wright type, so named by us because special functions of Mittag-Leffler and of Wright type appear in the definition of the relevant waiting times. We compare these three processes with each other, furthermore consider corresponding...

Risk-sensitive Markov stopping games with an absorbing state

Jaicer López-Rivero, Rolando Cavazos-Cadena, Hugo Cruz-Suárez (2022)

Kybernetika

This work is concerned with discrete-time Markov stopping games with two players. At each decision time player II can stop the game paying a terminal reward to player I, or can let the system to continue its evolution. In this latter case player I applies an action affecting the transitions and entitling him to receive a running reward from player II. It is supposed that player I has a no-null and constant risk-sensitivity coefficient, and that player II tries to minimize the utility of player I....

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