Related papers: Some applications of phase-type distributions in r…
A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with $n$ current particles, a new particle is born with instantaneous rate $\lambda_n$ and a particle…
Biomarker measurements obtained by blood sampling are often used as a non-invasive means of monitoring tumour progression in cancer patients. Diseases evolve dynamically over time, and studying longitudinal observations of specific…
Autoregressive processes are intensively studied in statistics and other fields of applied stochastics. For many applications the overshoot and the threshold-time are of special interest. When the upward innovations are in the class of…
In studies of recurrent events, joint modeling approaches are often needed to allow for potential dependent censoring by a terminal event such as death. Joint frailty models for recurrent events and death with an additional dependence…
In this article, we provide different representations for a time-fractional birth and death process $N_{\alpha}(t)$, whose transition probabilities are governed by a time-fractional system of differential equations. More specifically, we…
Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…
Joint modelling of longitudinal and survival data is increasingly used in clinical trials on cancer. In prostate cancer for example, these models permit to account for the link between longitudinal measures of prostate-specific antigen…
We consider a simple but important class of metastable discrete time Markov chains, which we call perturbed Markov chains. Basically, we assume that the transition matrices depend on a parameter $\varepsilon$, and converge as $\varepsilon$.…
The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…
We propose autoregressive Bayesian semi-parametric models for waiting times between recurrent events. The aim is two-fold: inference on the effect of possibly time-varying covariates on the gap times and clustering of individuals based on…
Many applications in medical statistics as well as in other fields can be described by transitions between multiple states (e.g. from health to disease) experienced by individuals over time. In this context, multi-state models are a popular…
This book handles the fatty liver disease from the bio-statistical point of view . It discusses the disease process in the simple general form of health-disease-death multi-states model . Continuous Time Markov Chains are used to estimate…
Catastrophe Markov chain population models have received a lot of attention in the recent past. We herewith consider two special cases of such models involving total disasters, both in discrete and in continuous-time. Depending on the…
This paper contributes an in-depth study of properties of continuous time Markov chains (CTMCs) on non-negative integer lattices $\N_0^d$, with particular interest in one-dimensional CTMCs with polynomial transitions rates. Such stochastic…
The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a…
As cancer patient survival improves, late effects from treatment are becoming the next clinical challenge. Chemotherapy and radiotherapy, for example, potentially increase the risk of both morbidity and mortality from second malignancies…
We consider a class of piecewise-deterministic Markov processes where the state evolves according to a linear dynamical system. This continuous time evolution is interspersed by discrete events that occur at random times and change (reset)…
We register a random sequence which has the following properties: it has three segments being the homogeneous Markov processes. Each segment has his own one step transition probability law and the length of the segment is unknown and…
Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest.…
Motility is characteristic of life, but a common basis for movement has remained to be identified. Diverse systems in motion shift between two states depending on interactions that turnover at the rate of an applied cycle of force. Although…