Related papers: A note on Wiener-Hopf factorization for Markov Add…
As in the paper [G. Groenewald, M.A. Kaashoek, A.C.M. Ran, Wiener-Hopf indices of unitary functions on the unit circle in terms of realizations and related results on Toeplitz operators. \emph{Indag. Math.} 28 (2017) 694--710] our aim is to…
We obtain an explicit representation for the Laplace transform of the waiting time for a wide class of distributions by solving the Wiener-Hopf factorization problem via the Hadamard product theorem. Under broad conditions it is shown that…
In Kuznetsov et al. (2011) a new Monte Carlo simulation technique was introduced for a large family of Levy processes that is based on the Wiener-Hopf decomposition. We pursue this idea further by combining their technique with the recently…
We introduce partial $r$-Bell polynomials in three combinatorial Hopf algebras. We prove a factorization formula for the generating functions which is a consequence of the Zassenhauss formula.
For a root system R, a field K and a "choice of coefficients in K" we define a category of graded spaces with operators and study some of its properties. Then we assume that the coefficients are given by quantum binomials. We use basic…
A vector-valued version of the Girsanov theorem is presented, for a scalar process with respect to a Banach-valued measure. Previously, a short discussion about the Birkhoff-type integration is outlined, as for example integration by…
Wiener-Hopf plus Hankel operators $W(a)+H(b):L^p(\mathbb{R}^+)\to L^p(\mathbb{R}^+)$ with generating functions $a$ and $b$ from a subalgebra of $L^\infty(\mathbb{R})$ containing almost periodic functions and Fourier images of…
We construct a family of genealogy-valued Markov processes that are induced by a continuous-time Markov population process. We derive exact expressions for the likelihood of a given genealogy conditional on the history of the underlying…
In this note we re-visit the fundamental question of the strong law of large numbers and central limit theorem for processes in continuous time with conditional stationary and independent increments. For convenience we refer to them as…
A factorization theory is proposed for Wiener-Hopf plus Hankel operators with almost periodic Fourier symbols. We introduce a factorization concept for the almost periodic Fourier symbols such that the properties of the factors will allow…
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…
The paper extends Birkhoff's theorem on doubly stochastic matrices to some countable families of discrete probability spaces with nonempty intersections. We join every two elements lying in the same probability space by an edge and…
A Monte Carlo method for computing the action of a matrix exponential for a certain class of matrices on a vector is proposed. The method is based on generating random paths, which evolve through the indices of the matrix, governed by a…
The addition relation for the Riemann theta functions and for its limits, which lead to the appearance of exponential functions in soliton type equations is discussed. The presented form of addition property resolves itself to the…
The Wiener-Hopf equations are a Toeplitz system of linear equations that naturally arise in several applications in time series. These include the update and prediction step of the stationary Kalman filter equations and the prediction of…
We consider additive functionals of Markov processes in continuous time with general (metric) state spaces. We derive concentration bounds for their exponential moments and moments of finite order. Applications include diffusions,…
The aim of this survey is twofold. First we show how the Markov tower construction is applicable for obtaining finer stochastic properties, like a local limit theorem of probability theory. Here the fundamental method is the study of the…
We present a direct derivation of the theorem of M. Maxwell and M. Woodroofe (Ann. Probab. 28 (2000) 713-724), on martingale approximation of additive functionals of stationary Markov processes, from the non-reversible version of the…
We extend the Marsden-Weinstein reduction theorem and the Darboux-Moser-Weinstein theorem to symplectic Lie algebroids. We also obtain a coisotropic embedding theorem for symplectic Lie algebroids.
A new probalistic approach to general relativistic kinetic theory is proposed. The general relativistic Boltzmann equation is linked to a new Markov process in a completely intrinsic way. This treatment is then used to prove the causal…