Related papers: A Markov property for set-indexed processes
Even simply-defined, finite-state generators produce stochastic processes that require tracking an uncountable infinity of probabilistic features for optimal prediction. For processes generated by hidden Markov chains the consequences are…
Comparison results for Markov processes w.r.t. function class induced (integral) stochastic orders have a long history. The most general results so far for this problem have been obtained based on the theory of evolution systems on Banach…
A mean-field extension of the queueing system \(GI/GI/1\) is considered. The process is constructed as a Markov solution of a martingale problem. Uniqueness in distribution is established under a bit different sets of assumptions on…
This paper considers the problem of defining distributions over graphical structures. We propose an extension of the hyper Markov properties of Dawid and Lauritzen [Ann. Statist. 21 (1993) 1272-1317], which we term structural Markov…
The Markov property is widely imposed in analysis of time series data. Correspondingly, testing the Markov property, and relatedly, inferring the order of a Markov model, are of paramount importance. In this article, we propose a…
Attribution techniques explain the outcome of an AI model by assigning a numerical score to its inputs. So far, these techniques have mainly focused on attributing importance to static input features at a single point in time, and thus fail…
This paper considers a simulation-based estimator for a general class of Markovian processes and explores some strong consistency properties of the estimator. The estimation problem is defined over a continuum of invariant distributions…
We introduce the minimal maximally predictive models ({\epsilon}-machines) of processes generated by certain hidden semi-Markov models. Their causal states are either hybrid discrete-continuous or continuous random variables and…
We define the concept of an `open' Markov process, a continuous-time Markov chain equipped with specified boundary states through which probability can flow in and out of the system. External couplings which fix the probabilities of…
The analysis of many problems of interest associated with Markov chains, e.g. stationary distributions, moments of first passage time distributions and moments of occupation time random variables, involves the solution of a system of linear…
In this paper is proved the limit theorem for randomly indexed sequence of random processes in the case where sequences of random index and random processes are independent, also the estimation of convergence rate is obtained.
We define a Markov process on the set of countable graphs with spins. Transitions are local substitutions in the graph. It is proved that the scaling macrodimension is an invariant of such dynamics.
We prove a complete class theorem that characterizes \emph{all} stationary time reversible Markov processes whose finite dimensional marginal distributions (of all orders) are infinitely divisible. Aside from two degenerate cases (iid and…
This paper introduces the concept of a generating set for stochastic matrices -- a subset of matrices whose repeated composition generates the entire set. Understanding such generating sets requires specifying the "indivisible elements" and…
A continuous-time Markov process $X$ can be conditioned to be in a given state at a fixed time $T > 0$ using Doob's $h$-transform. This transform requires the typically intractable transition density of $X$. The effect of the $h$-transform…
We study the evolution of a particle system whose genealogy is given by a supercritical continuous time Galton--Watson tree. The particles move independently according to a Markov process and when a branching event occurs, the offspring…
This article considers a model for alternative processes for securities prices and compares this model with actual return data of several securities. The distributions of returns that appear in the model can be Gaussian as well as…
We observe the continuous-time Markov Branching Process without high-order moments and allowing Immigration. Limit properties of transition functions and their convergence to invariant measures are investigated. Main mathematical tool is…
Diffusion models are typically trained using score matching, a learning objective agnostic to the underlying noising process that guides the model. This paper argues that Markov noising processes enjoy an advantage over alternatives, as the…
In stochastic models for queues and their networks, random events evolve in time. A process for their backward evolution is referred to as a time reversed process. It is often greatly helpful to view a stochastic model from two different…