Related papers: Self-duality of Markov processes and intertwining …

We study non-selfadjoint representations of a finite dimensional real Lie algebra $\fg$. To this end we embed a non-selfadjoint representation of $\fg$ into a more complicated structure, that we call a $\fg$-operator vessel and that is…

We develop a canonical pairing between trees and graphs, which passes to their quotients by Jacobi identities. This pairing is an effective and simple tool for understanding the Lie and Poisson operads, providing canonical duals. In the…

Our main result is the martingale representations for Markov additive processes where the modulator is a Levy process. These processes have three parts: the modulator, the jumps of the ordinate triggered by the modulator, and the…

Constrained Markov processes, such as reflecting diffusions, behave as an unconstrained process in the interior of a domain but upon reaching the boundary are controlled in some way so that they do not leave the closure of the domain. In…

It was recently shown that the theory of linear stochastic systems can be viewed as a particular case of the theory of linear systems on a certain commutative ring of power series in a countable number of variables. In the present work we…

We study a Lax pair in a $2$-parameter Lie algebra in various representations. The overlap coefficients of the eigenfunctions of $L$ and the standard basis are given in terms of orthogonal polynomials and orthogonal functions. Moreover,…

A Markov Additive Process is a bi-variate Markov process $(\xi,J)=\big((\xi_t,J_t),t\geq0\big)$ which should be thought of as a multi-type L\'evy process: the second component $J$ is a Markov chain on a finite space $\{1,\ldots,K\}$, and…

This paper considers discretization of the L\'evy process appearing in the Lamperti representation of a strictly positive self-similar Markov process. Limit theorems for the resulting approximation are established under some regularity…

There is a commutative algebra of differential-difference operators, acting on polynomials on R_2, associated with the reflection group B2. This paper presents an integral transform which intertwines this algebra, allowing one free…

In an earlier paper we introduced a notion of Markov automaton, together with parallel operations which permit the compositional description of Markov processes. We illustrated by showing how to describe a system of n dining philosophers,…

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…

We study discretizations of polynomial processes using finite state Markov processes satisfying suitable moment matching conditions. The states of these Markov processes together with their transition probabilities can be interpreted as…

It is shown that two braids represent transversally isotopic links if and only if one can pass from one braid to another by conjugations in braid groups, positive Markov moves, and their inverses.

We investigate aspects of semimartingale decompositions, approximation and the martingale representation for multidimensional correlated Markov processes. A new interpretation of the dependence among processes is given using the martingale…

Theory of differential operators on associative algebras is not extended to the non-associative ones in a straightforward way. We consider differential operators on Lie algebras. A key point is that multiplication in a Lie algebra is its…

We produce counterexamples to show that in the definition of the notion of intertwining operator for modules for a vertex operator algebra, the commutator formula cannot in general be used as a replacement axiom for the Jacobi identity. We…

We characterize all multi-dimensional real self-similar Gaussian Markov processes. Three types of covariance matrix functions occur: white-noise type functions, covariances that can be expressed by continuous matrix semigroups, and…

Markov combination is an operation that takes two statistical models and produces a third whose marginal distributions include those of the original models. Building upon and extending existing work in the Gaussian case, we develop Markov…

We analyse various properties of stochastic Markov processes with multiplicative white noise. We take a single-variable problem as a simple example, and we later extend the analysis to the Landau-Lifshitz-Gilbert equation for the stochastic…

We construct a family of self-similar Markov martingales with given marginal distributions. This construction uses the self-similarity and Markov property of a reference process to produce a family of Markov processes that possess the same…