Related papers: Thiele's Differential Equation Based on Markov Jum…
Inspired by a duration-dependent life insurance model, we consider continuous-time semi-Markov jump processes, initially assumed to have a finite state-space. We develop approximations using jump processes that are time-homogeneous Markov,…
A multi--state life insurance model is naturally described in terms of the intensity matrix of an underlying (time--inhomogeneous) Markov process which describes the dynamics for the states of an insured person. Between and at transitions,…
Markov jump processes are continuous-time stochastic processes with a wide range of applications in both natural and social sciences. Despite their widespread use, inference in these models is highly non-trivial and typically proceeds via…
We consider a Markov jump process on a general state space to which we apply a time-dependent weak perturbation over a finite time interval. By martingale-based stochastic calculus, under a suitable exponential moment bound for the…
Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…
We consider the modeling of data generated by a latent continuous-time Markov jump process with a state space of finite but unknown dimensions. Typically in such models, the number of states has to be pre-specified, and Bayesian inference…
Point and interval estimation of future disability inception and recovery rates are predominantly carried out by combining generalized linear models (GLM) with time series forecasting techniques into a two-step method involving parameter…
We are interested in the connection between a metastable continuous state space Markov process (satisfying e.g. the Langevin or overdamped Langevin equation) and a jump Markov process in a discrete state space. More precisely, we use the…
We consider exchangeable Markov multi-state survival processes -- temporal processes taking values over a state-space$\mathcal{S}$ with at least one absorbing failure state $\flat \in \mathcal{S}$ that satisfy natural invariance properties…
Disability insurance claims are often affected by lengthy reporting delays and adjudication processes. The classic multistate life insurance modeling framework is ill-suited to handle such information delays since the cash flow and…
A possibly time-dependent transition intensity matrix or generator $(Q(t))$ characterizes the law of a Markov jump process (MP). For a time homogeneous MP, the transition probability matrix (TPM) can be expressed as a matrix exponential of…
This paper develops a new class of conditional Markov jump processes with regime switching and paths dependence. The key novel feature of the developed process lies on its ability to switch the transition rate as it moves from one state to…
We consider a piecewise deterministic Markov decision process, where the expected exponential utility of total (nonnegative) cost is to be minimized. The cost rate, transition rate and post-jump distributions are under control. The state…
Piecewise-deterministic Markov processes form a general class of non-diffusion stochastic models that involve both deterministic trajectories and random jumps at random times. In this paper, we state a new characterization of the jump rate…
Switching dynamical systems are an expressive model class for the analysis of time-series data. As in many fields within the natural and engineering sciences, the systems under study typically evolve continuously in time, it is natural to…
We have studied Markov processes on denumerable state space and continuous time. We found that all these processes are connected via gauge transformations. We have used this result before as a method for resolution of equations, included…
In this work, a versatile mathematical framework for multi-state probabilistic modeling of Resistive Switching (RS) devices is proposed for the first time. The mathematical formulation of memristor and Markov jump processes are combined…
Thiele's differential equation explains the change in prospective reserve and plays a fundamental role in safe-side calculations and other types of actuarial model comparisons. This paper presents a `model lean' version of Thiele's equation…
Markov chains provide a foundational framework for modeling sequential stochastic processes, with the transition probability matrix characterizing the dynamics of state evolution. While classical estimation methods such as maximum…
We propose a unified framework that extends the inference methods for classical hidden Markov models to continuous settings, where both the hidden states and observations occur in continuous time. Two different settings are analyzed: hidden…