Related papers: On discrete-time semi-Markov processes
Modeling the time evolution of discrete sets of items (e.g., genetic mutations) is a fundamental problem in many biomedical applications. We approach this problem through the lens of continuous-time Markov chains, and show that the…
The deterministic analog of the Markov property of a time-homogeneous Markov process is the semigroup property of solutions of an autonomous differential equation. The semigroup property arises naturally when the solutions of a differential…
We study continuous time Markov processes on graphs. The notion of frequency is introduced, which serves well as a scaling factor between any Markov time of a continuous time Markov process and that of its jump chain. As an application, we…
In this study, a new extension of the Markov Renewal theory is introduced by allowing time to evolve in multiple dimensions. The resulting chains are referred to as multi-time Markov Renewal chains and since this extension is new, the state…
We study the large deviations of the time-integrated current for a self-propelled particle moving within a confined environment. The dynamics is modeled as a semi-Markovian process, where the transitions between a \textit{normal running…
For a wide class of continuous-time Markov processes, including all irreducible hypoelliptic diffusions evolving on an open, connected subset of $\RL^d$, the following are shown to be equivalent: (i) The process satisfies (a slightly weaker…
This paper establishes explicit solutions for fractional diffusion problems on bounded domains. It also gives stochastic solutions, in terms of Markov processes time-changed by an inverse stable subordinator whose index equals the order of…
We present a numerical method to compute expectations of functionals of a piecewise-deterministic Markov process. We discuss time dependent functionals as well as deterministic time horizon problems. Our approach is based on the…
We consider the discrete-time migration-recombination equation, a deterministic, nonlinear dynamical system that describes the evolution of the genetic type distribution of a population evolving under migration and recombination in a law of…
We develop theory and applications of forward characteristic processes in discrete time following a seminal paper of Jan Kallsen and Paul Kr\"uhner. Particular emphasis is placed on the dynamics of volatility surfaces which can be easily…
Markov models are often used to capture the temporal patterns of sequential data for statistical learning applications. While the Hidden Markov modeling-based learning mechanisms are well studied in literature, we analyze a…
Recent works in Learning-Based Model Predictive Control of dynamical systems show impressive sample complexity performances using criteria from Information Theory to accelerate the learning procedure. However, the sequential exploration…
A discrete time branching process where the offspring distribution is generation-dependent, and the number of reproductive individuals is controlled by a random mechanism is considered. This model is a Markov chain but, in general, the…
We formalize and analyze the notions of stochastic monotonicity and realizable mono-tonicity for Markov Chains in continuous-time, taking values in a finite partially ordered set. Similarly to what happens in discrete-time, the two notions…
We analyze the notions of monotonicity and complete monotonicity for Markov Chains in continuous-time, taking values in a finite partially ordered set. Similarly to what happens in discrete-time, the two notions are not equivalent. However,…
We treat the class of universal Markov processes on the d-dimensional Euklidean space which do not depend on random. For these, as well as for several subclasses, we prove criteria whether a function f, defined on the positive half-line,…
In this paper Fokker-Planck-Kolmogorov type equations associated with stochastic differential equations driven by a time-changed fractional Brownian motion are derived. Two equivalent forms are suggested. The time-change process considered…
The stochastic properties of a Langevin-type Markov process can be extracted from a given time series by a Markov analysis. Also processes that obey a stochastically forced second order differential equation can be analyzed this way by…
In this paper, we consider semi-Markov processes whose transition times and transition probabilities depend on a small parameter $\varepsilon$. Understanding the asymptotic behavior of such processes is needed in order to study the…
We consider the generalized time-dependent Schr\"odinger equation on the half-axis and a broad family of finite-difference schemes with the discrete transparent boundary conditions (TBCs) to solve it. We first rewrite the discrete TBCs in a…