Related papers: Conditioned real self-similar Markov processes

Let $X$ be a Markov process taking values in $\mathbf{E}$ with continuous paths and transition function $(P_{s,t})$. Given a measure $\mu$ on $(\mathbf{E}, \mathscr{E})$, a Markov bridge starting at $(s,\varepsilon_x)$ and ending at…

Borrowing ideas from open quantum systems, we describe a formalism to encode ensembles of trajectories of classical stochastic dynamics in terms of continuous matrix product states (cMPSs). We show how to define in this approach "biased" or…

We develop a first-order (pseudo-)gradient approach for optimizing functions over the stationary distribution of discrete-time Markov chains (DTMC). We give insights into why solving this optimization problem is challenging and show how…

This paper deals with the output regulation problem (ORP) of a linear time-invariant (LTI) system in the presence of sporadically sampled measurement streams with the inter-sampling intervals following a stochastic process. Under such…

We consider periodic Markov chains with absorption. Applying to iterates of this periodic Markov chain criteria for the exponential convergence of conditional distributions of aperiodic absorbed Markov chains, we obtain exponential…

In this paper we consider random dynamical systems formed by concatenating maps acting on the unit interval $[0,1]$ in an iid fashion. Considered as a stationary Markov process, the random dynamical system possesses a unique stationary…

An infinite system of point particles placed in $\mathds{R}^d$ is studied. The particles are of two types; they perform random walks in the course of which those of distinct types repel each other. The interaction of this kind induces an…

In this paper we show how questions about operator algebras constructed from stochastic matrices motivate new results in the study of harmonic functions on Markov chains. More precisely, we characterize coincidence of conditional…

The master equation and, more generally, Markov processes are routinely used as models for stochastic processes. They are often justified on the basis of randomization and coarse-graining assumptions. Here instead, we derive n-th order…

We propose and analyze a class of particle methods for the Vlasov equation with a strong external magnetic field in a torus configuration. In this regime, the time step can be subject to stability constraints related to the smallness of…

We describe the solution of an optimal stopping problem for a stable L\'evy process killed at state-dependent rate, which can be seen as a model for bankruptcy. The killing rate is chosen in such a way that the killed process remains…

The time at which a one-dimensional continuous strong Markov process attains a boundary point of its state space is a discontinuous path functional and it is, therefore, unclear whether the exit time can be approximated by hitting times of…

The slow processes of metastable stochastic dynamical systems are difficult to access by direct numerical simulation due the sampling problem. Here, we suggest an approach for modeling the slow parts of Markov processes by approximating the…

We propose a method for approximating solutions to optimization problems involving the global stability properties of parameter-dependent continuous-time autonomous dynamical systems. The method relies on an approximation of the…

We study the so-called two-time-scale stochastic approximation, a simulation-based approach for finding the roots of two coupled nonlinear operators. Our focus is to characterize its finite-time performance in a Markov setting, which often…

We analyze asymptotically a differential-difference equation, that arises in a Markov-modulated fluid model. Here there are N identical sources that turn "on" and "off", and when "on" they generate fluid at unit rate into a buffer, which…

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…

We analyse a model of Hes1 gene transcription and protein synthesis with a negative feedback loop. The effect of multiple binding sites in the Hes1 promoter as well as the dimer formation process are taken into account. We consider three,…

This work derives a theoretical value for the entropy of a Linear Additive Markov Process (LAMP), an expressive model able to generate sequences with a given autocorrelation structure. While a first-order Markov Chain model generates new…

For a class of stochastic differential equations with reflection for which a certain ${\mathbb{L}}^p$ continuity condition holds with $p>1$, it is shown that any weak solution that is a strong Markov process can be decomposed into the sum…