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The e-Property of Asymptotically Stable Markov Semigroups
The relations between asymptotic stability, the eventual e-property and the e-property of Markov semigroups, acting on measures defined on general...
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Stop** Times and the Strong Markov Property
Given a stop** time τ, the Markov property for discrete parameter Markov processes is extended to the conditional distribution of the process...
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Relation Between the Eventual Continuity and the E-property for Markov-Feller Semigroups
We investigate some relations between two kinds of semigroup regularities, namely the e-property and the eventual continuity, both of which...
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Estimation and Strong Approximation of Hidden Markov Models
We give novel conditions for the existence of the limit of the normalized log-likelihood function for a finite-state continuous read-out Hidden...
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Strong Feller semigroups and Markov processes: a counterexample
The aim of this note is to show, by providing an elementary way to construct counterexamples, that the strong Feller and the joint (space-time)...
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Tree-Indexed Markov Chains in Random Environment and Some of Their Strong Limit Properties
In this paper, the authors first introduce the tree-indexed Markov chains in random environment, which takes values on a general state space. Then,...
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Mixing times and hitting times for general Markov processes
The hitting and mixing times are two fundamental quantities associated with Markov chains. In Peres and Sousi [PS15] and Oliveira [Oli12], the...
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A Review of Martingales, Stop** Times, and the Markov Property
Among the dominant notions from the theory of stochastic processes used to develop the theory of stochastic differential equations are those of...
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Fuzzy Observables: from Weak Markov Kernels to Markov Kernels
We provide a proof based on transfinite induction that every weak Markov kernel is equivalent to a Markov kernel. We only assume the space where the...
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Random Walk, Brownian Motion, and the Strong Markov Property
In this chapter the strong Markov property is derived as an extension of the Markov property to certain random times, called stop** times. A number...
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On the Transfinite Symmetric Strong Diameter Two Property
We study transfinite analogues of the symmetric strong diameter two property . We investigate the stability of these properties under
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Faking Brownian motion with continuous Markov martingales
Hamza and Klebaner
(2007) [10] posed the problem of constructing martingales with one-dimensional Brownian marginals that differ from Brownian... -
Markov Chains
This graphical interpretation of a Markov chain in terms of a “random walk” on a set E is adapted to the study of random walks on graphs. Since the...
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Markov risk map**s and risk-sensitive optimal prediction
We formulate a probabilistic Markov property in discrete time under a dynamic risk framework with minimal assumptions. This is useful for recursive...
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The structure of the local time of Markov processes indexed by Lévy trees
We construct an additive functional playing the role of the local time—at a fixed point x —for Markov processes indexed by Lévy trees. We start by...
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Path continuity of Markov processes and locality of Kolmogorov operators
We prove that if we are given a generator of a right Markov process with càdlàg paths and an open domain G in the state space, on which the generator...
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Potential theory for quantum Markov states and other quantum Markov chains
We introduce a potential theory for a class of Quantum Markov Chains whose forward and backward Markov transition operators satisfy a special...
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Markov Chains
This chapter is devoted to Markov chains with values in a finite or countable state space. Using the strong Markov property, we investigate recurrent...
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Constrained Markov Decision Processes with Non-constant Discount Factor
This paper studies constrained Markov decision processes under the total expected discounted cost optimality criterion, with a state-action dependent...
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Free gs-Monoidal Categories and Free Markov Categories
Categorical probability has recently seen significant advances through the formalism of Markov categories, within which several classical theorems...
