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Many researchers have investigated first hitting times as models for survival data. First hitting times arise naturally in many types of stochastic processes, ranging from Wiener processes to Markov chains. In a survival context, the state…

Methodology · Statistics 2009-09-29 Mei-Ling Ting Lee , G. A. Whitmore

A new class of distributions based on phase-type distributions is introduced in the current paper to model lifetime data in the field of reliability analysis. This one is the natural extension of the distribution proposed by Acal et al.…

Methodology · Statistics 2025-01-13 Juan Eloy Ruiz-Castro , Christian Acal , Juan B. Roldán

We introduce a novel class of bivariate common-shock discrete phase-type (CDPH) distributions to describe dependencies in loss modeling, with an emphasis on those induced by common shocks. By constructing two jointly evolving terminating…

Statistics Theory · Mathematics 2026-01-14 Martin Bladt , Eric C. K. Cheung , Oscar Peralta , Jae-Kyung Woo

Survival models are a popular tool for the analysis of time to event data with applications in medicine, engineering, economics, and many more. Advances like the Cox proportional hazard model have enabled researchers to better describe…

Machine Learning · Statistics 2021-02-16 Stefan Groha , Sebastian M Schmon , Alexander Gusev

We study a class of Markov processes with finite state space and continuous time that have product form stationary distributions. We obtain a number of examples that can generate conjectures for diffusions with inert drift.

Probability · Mathematics 2008-10-19 Krzysztof Burdzy , David White

Let $X_1,X_2,...$ be a sequence of random variables satisfying the distributional recursion $X_1=0$ and $X_n= X_{n-I_n}+1$ for $n=2,3,...$, where $I_n$ is a random variable with values in $\{1,...,n-1\}$ which is independent of…

Probability · Mathematics 2007-11-01 Alex Iksanov , Martin Möhle

Continuous-time Markov chains describing interacting processes exhibit a state space that grows exponentially in the number of processes. This state-space explosion renders the computation or storage of the time-marginal distribution, which…

Numerical Analysis · Mathematics 2020-06-16 Peter Georg , Lars Grasedyck , Maren Klever , Rudolf Schill , Rainer Spang , Tilo Wettig

Because failures in distribution systems caused by extreme weather events directly result in consumers' outages, this paper proposes a state-based decision-making model with the objective of mitigating loss of load to improve the…

Optimization and Control · Mathematics 2019-04-02 Chong Wang , Ping Ju , Shunbo Lei , Zhaoyu Wang , Yunhe Hou

Event of the same type occurring several times for one individual (recurrent events) are present in various domains (industrial systems reliability, episodes of unemployment, political conflicts, chronic diseases episodes). Analysis of such…

Applications · Statistics 2024-01-24 Génia Babykina , Vincent Vandewalle

State-switching models such as hidden Markov models or Markov-switching regression models are routinely applied to analyse sequences of observations that are driven by underlying non-observable states. Coupled state-switching models extend…

Reinforced processes are known to provide a stochastic representation for the quasi-stationary distribution of a given killed Markov process - describing the killed Markov process at fixed time instants. In this paper we shall adapt the…

Probability · Mathematics 2022-02-10 Oliver Tough

We consider a non-attractive three state contact process on $\mathbb Z$ and prove that there exists a regime of survival as well as a regime of extinction. In more detail, the process can be regarded as an infection process in a dynamic…

Probability · Mathematics 2017-06-27 Marinus Gottschau , Markus Heydenreich , Kilian Matzke , Cristina Toninelli

To ensure the effective and objective development of transportation networks, it is crucial to identify performance limitations across various subsystems. A timetable-independent assessment of infrastructure capacity at railway junctions is…

Systems and Control · Electrical Eng. & Systems 2025-05-27 Tamme Emunds , Nils Nießen

Dynamic epidemic models have proven valuable for public health decision makers as they provide useful insights into the understanding and prevention of infectious diseases. However, inference for these types of models can be difficult…

Methodology · Statistics 2018-10-30 Theresa Stocks

We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. We give explicit formulas for probability generating functions, and also for means, variances and state…

Probability · Mathematics 2019-10-30 Luisa Beghin , Claudio Macci , Barbara Martinucci

This paper presents a stochastic model motivated by the study of a virus-like evolving population with different mutation rates. This is a continuous time birth-death model: the birth processes are mutually-exciting Hawkes processes and the…

Probability · Mathematics 2026-03-10 Rahul Roy , Dharmaraja Selvamuthu , Paola Tardelli

Multi-state capture-recapture data comprise individual-specific sighting histories together with information on individuals' states related, for example, to breeding status, infection level, or geographical location. Such data are often…

Applications · Statistics 2023-11-16 Sina Mews , Roland Langrock , Ruth King , Nicola Quick

Multistate Markov models are a canonical parametric approach for data modeling of observed or latent stochastic processes supported on a finite state space. Continuous-time Markov processes describe data that are observed irregularly over…

We study a model of a polling system, that is, a collection of $d$ queues with a single server that switches from queue to queue. The service time distribution and arrival rates change randomly every time a queue is emptied. This model is…

Probability · Mathematics 2007-11-06 Iain MacPhee , Mikhail Menshikov , Dimitri Petritis , Serguei Popov

We consider a hybrid method to simulate the return time to the initial state in a critical-case birth--death process. The expected value of this return time is infinite, but its distribution asymptotically follows a power-law. Hence, the…

Methodology · Statistics 2024-12-20 Krzysztof Bartoszek