Related papers: On Marginal Markov Processes of Quantum Quadratic …

We introduce and study a family of Markov processes on partitions. The processes preserve the so-called z-measures on partitions previously studied in connection with harmonic analysis on the infinite symmetric group. We show that the…

This paper deals with the problem of measurable lifting modification for stochastic processes in its most general form and with the 'product lifting problem'. Solutions to the positive are reduced to the existence of marginals with respect…

We give a short overview of recent results on a specific class of Markov process: the Piecewise Deterministic Markov Processes (PDMPs). We first recall the definition of these processes and give some general results. On more specific cases…

The Laplace transform of partial sums of the square of a non-centered Gauss-Markov process, conditioning on its starting point, is explicitly computed. The parameters of multiplicative ergodicity are deduced.

In the development of stochastic integration and the theory of semimartingales, Markov processes have been a constant source of inspiration. Despite this historical interweaving, it turned out that semimartingales should be considered the…

We exhibit conditions under which the flow of marginal distributions of a discontinuous semimartingale $\xi$ can be matched by a Markov process, whose infinitesimal generator is expressed in terms of the local characteristics of $\xi$. Our…

We consider a stochastic process which is (a) described by a continuous-time Markov chain on only short time-scales and (b) constrained to conserve a number of hidden quantities on long time-scales. We assume that the transition matrix of…

We present limit theorems for a sequence of Piecewise Deterministic Markov Processes (PDMPs) taking values in a separable Hilbert space. This class of processes provides a rigorous framework for stochastic spatial models in which discrete…

We discuss the conceptually different definitions used for the non-Markovianity of classical and quantum processes. The well-established definition for non-Markovianity of a classical stochastic process represents a condition on the…

We present a short introduction into the framework of piecewise deterministic Markov processes. We illustrate the abstract mathematical setting with a series of examples related to dispersal of biological systems, cell cycle models, gene…

Stochastic processes abound in nature and accurately modeling them is essential across the quantitative sciences. They can be described by hidden Markov models (HMMs) or by their quantum extensions (QHMMs). These models explain and give…

To make sense of the world around us, we develop models, constructed to enable us to replicate, describe, and explain the behaviours we see. Focusing on the broad case of sequences of correlated random variables, i.e., classical stochastic…

Let $\mu$ = ($\mu$t)t$\in$R be a 1-parameter family of probability measures on R. In [11] we introduced its ``Markov-quantile''process: a process X= (Xt)t$\in$R that resembles as much as possible the quantile process attached to $\mu$,…

We present quantum observable Markov decision processes (QOMDPs), the quantum analogues of partially observable Markov decision processes (POMDPs). In a QOMDP, an agent's state is represented as a quantum state and the agent can choose a…

The time evolution of the one-point probability vector of stochastic processes and quantum processes for $N$-level systems have been unified. Hence, quantum states and quantum operations can be regarded as generalizations of the one-point…

This paper shows a novel way of simulating a Markov process by a quantum computer. The main purpose of the paper is to show a particular application of quantum computing in the field of stochastic processes analysis. Using a Quantum…

We suggest to investigate certain non-standard (pseudo-)differential operators in order to construct and to study multi-parameter processes. Our approach will include "classical" multi-parameter Markov processes but will go eventually far…

We consider a Markov process on non-negative integer arrays of a certain shape, this shape being determined by general parameters in the model which correspond to drifts. In the case where these drifts are trivial, the arrays are reverse…

In this note, we present few examples of Piecewise Deterministic Markov Processes and their long time behavior. They share two important features: they are related to concrete models (in biology, networks, chemistry,. . .) and they are…

Stochastic convergence of discrete time Markov processes has been analysed based on a dual Lyapunov approach. Using some existing results on ergodic theory of Markov processes, it has been shown that existence of a properly subinvariant…