Related papers: Strong Stationary Duality for Diffusion Processes

The large deviations at Level 2.5 are applied to Markov processes with absorbing states in order to obtain the explicit extinction rate of metastable quasi-stationary states in terms of their empirical time-averaged density and of their…

We study the large deviations of current-type observables defined for Markov diffusion processes evolving in smooth bounded regions of $\mathbb{R}^d$ with reflections at the boundaries. We derive for these the correct boundary conditions…

We consider stochastic motion of a particle on a cyclic graph with arbitrarily periodic time dependent kinetic rates. We demonstrate duality relations for statistics of currents in this model and in its continuous version of a diffusion in…

We consider a class of discrete time Markov chains with state space [0,1] and the following dynamics. At each time step, first the direction of the next transition is chosen at random with probability depending on the current location. Then…

We find all factorized duality functions for a class of interacting particle systems. The functions we recover are self-duality functions for interacting particle systems such as zero-range processes, symmetric inclusion and exclusion…

Diffusion models offer stable training and state-of-the-art performance for deep generative modeling tasks. Here, we consider their use in the context of multivariate subsurface modeling and probabilistic inversion. We first demonstrate…

We analyse diffusion dynamics on weakly-coupled networks (interconnected networks) by means of separation of time scales. Using an adiabatic approximation we reduced the system dynamics to a Markov chain with aggregated variables and…

We study the stirring process with $N-1$ species on a generic graph $G=(V,\mathcal{E})$ with reservoirs. The multispecies stirring process generalizes the symmetric exclusion process, which is recovered in the case $N=2$. We prove the…

We use duality techniques - specifically Siegmund and Bernstein duality - as tools to analyse ergodic and recurrence properties of $[0,1]$-valued Markov processes. These dualities enable the derivation of sharp bounds on the distance to…

In the course of Darwinian evolution of a population, punctualism is an important phenomenon whereby long periods of genetic stasis alternate with short periods of rapid evolutionary change. This paper provides a mathematical interpretation…

In [4], we examined the use of coupling to obtain bounds on the mixing time of statistics on Markov chains. In the present paper, we consider the same general problem, but using strong stationary times rather than coupling. We discuss…

Information relaxation and duality in Markov decision processes have been studied recently by several researchers with the goal to derive dual bounds on the value function. In this paper we extend this dual formulation to controlled Markov…

A Markov process fluctuating away from its typical behavior can be represented in the long-time limit by another Markov process, called the effective or driven process, having the same stationary states as the original process conditioned…

In many applications, for example when computing statistics of fast subsystems in a multiscale setting, we wish to find the stationary distributions of systems of continuous time Markov chains. Here we present a class of models that appears…

A large deviation principle is established for a two-scale stochastic system in which the slow component is a continuous process given by a small noise finite dimensional It\^{o} stochastic differential equation, and the fast component is a…

Diffusion models have achieved huge empirical success in data generation tasks. Recently, some efforts have been made to adapt the framework of diffusion models to discrete state space, providing a more natural approach for modeling…

Previously, we demonstrated that the dynamics of kicked spin chains possess a remarkable duality property. The trace of the unitary evolution operator for $N$ spins at time $T$ is related to one of a non-unitary evolution operator for $T$…

We study quasi-stationary distributions and quasi-limiting behavior of Markov chains in general reducible state spaces with absorption. We propose a set of assumptions dealing with particular situations where the state space can be…

In this paper we consider the distribution of the location of the path supremum in a fixed interval for self-similar processes with stationary increments. To this end, a point process is constructed and its relation to the distribution of…

In the present Short Note an idea is proposed to explain the emergence and the observation of processes in complex media that are driven by fractional non-Markovian master equations. Particle trajectories are assumed to be solely Markovian…