Related papers: Some Conclusions on Markov Matrices and Transforma…
Stochastic matrices and positive maps in matrix algebras proved to be very important tools for analysing classical and quantum systems. In particular they represent a natural set of transformations for classical and quantum states,…
Consider a stochastic process $\{X(t)\}$ on a finite state space $ {\sf X}=\{1,\dots, d\}$. It is conditionally Markov, given a real-valued `input process' $\{\zeta(t)\}$. This is assumed to be small, which is modeled through the scaling,…
We justify and discuss expressions for joint lower and upper expectations in imprecise probability trees, in terms of the sub- and supermartingales that can be associated with such trees. These imprecise probability trees can be seen as…
It is common, when dealing with quantum processes involving a subsystem of a much larger composite closed system, to treat them as effectively memory-less (Markovian). While open systems theory tells us that non-Markovian processes should…
General birth-and-death as well as hopping stochastic dynamics of infinite particle systems in the continuum are considered. We derive corresponding evolution equations for correlation functions and generating functionals. General…
We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…
In this paper, we study a notion of local stationarity for discrete time Markov chains which is useful for applications in statistics. In the spirit of some locally stationary processes introduced in the literature, we consider triangular…
We study a class of multi-stage stochastic programs, which incorporate modeling features from Markov decision processes (MDPs). This class includes structured MDPs with continuous action and state spaces. We extend policy graphs to include…
By modeling the interaction of an open quantum system with its environment through a natural generalization of the classical concept of continuous time random walk, we derive and characterize a class of non-Markovian master equations whose…
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.
Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…
This paper consists of four parts. In the first part, we explain what eigenvalues we are interested in and show the difficulties of the study on the first (non-trivial) eigenvalue through examples. In the second part, we present some (dual)…
The embedding problem of Markov matrices in Markov semigroups is a classic problem that regained a lot of impetus and activities through recent needs in phylogeny and population genetics. Here, we give an account for dimensions $d\leqslant…
Random sampling of large Markov matrices with a tunable spectral gap, a nonuniform stationary distribution, and a nondegenerate limiting empirical spectral distribution (ESD) is useful. Fix $c>0$ and $p>0$. Let $A_n$ be the adjacency matrix…
Convenient parameterizations of matrices in terms of vectors transform (certain classes of) matrix equations into covariant (hence rotation-invariant) vector equations. Certain recently introduced such parameterizations are tersely…
Improved rates of convergence for ergodic homogeneous Markov chains are studied. In comparison to the earlier papers the setting is also generalised to the case without a unique dominated measure. Examples are provided where the new bound…
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…
In a real life process evolving over time, the relationship between its relevant variables may change. Therefore, it is advantageous to have different inference models for each state of the process. Asymmetric hidden Markov models fulfil…
Orthogonal Mueller matrices can be considered either as corresponding to retarders or to generalized transformations of the polarization basis for the representation of Stokes vectors, so that they constitute the only type of Mueller…
We prove pathwise large-deviation principles of switching Markov processes by exploiting the connection to associated Hamilton-Jacobi equations, following Jin Feng's and Thomas Kurtz's method. In the limit that we consider, we show how the…