相关论文: A note on Sarnak processes
A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expression of these numbers with symmetric function is deduced.
We obtain similar types of conclusions as that of Br\"{u}ck [1] for two differential polynomials which in turn radically improve and generalize several existing results. Moreover, a number of examples have been exhibited to justify the…
We study a class of Markov processes with finite state space and continuous time that have product form stationary distributions. We obtain a number of examples that can generate conjectures for diffusions with inert drift.
Superpositions of Ornstein-Uhlenbeck type (supOU) processes form a rich class of stationary processes with a flexible dependence structure. The asymptotic behavior of the integrated and partial sum supOU processes can be, however, unusual.…
Some combinatorial properties of fixed boundary rhombus random tilings with octagonal symmetry are studied. A geometrical analysis of their configuration space is given as well as a description in terms of discrete dynamical systems, thus…
In this note, we prove a conditionally centered version of the quenched weak invariance principle under the Hannan condition, for stationary processes. In the course, we obtain a (new) construction of the fact that any stationary process…
We study the structure of quantum Markov Processes from the point of view of product systems and their representations.
Motivated by Sarnak's conjecture on M\"obius orthogonality, we investigate the general problem of orthogonality for a bounded sequence to topological models of characteristic classes of measure-preserving automorphisms. Our main observation…
This paper is a continuation of our previous research on quadratic harnesses, that is, processes with linear regressions and quadratic conditional variances. Our main result is a construction of a Markov process from given orthogonal and…
This paper is a short introduction to orthogonal polynomials, both the general theory and some special classes. It ends with some remarks about the usage of computer algebra for this theory.
These notes derive a number of technical results on nonlinear contraction theory, a comparatively recent tool for system stability analysis. In particular, they provide new results on the preservation of contraction through system…
In this paper, we study a general Syracuse problem. We give some necessary conditions concerning the existence of eventual non trivial cycles. Some properties based on linear logarithmic forms are established. New general conjectures are…
The mechanics of the structured particles develops. The substantiation of applicability of such mechanics for the description of processes of evolution in open nonequilibrium systems is offered. The consequences following from the equations…
This paper reproduces results from Chapter 11 of the forthcoming book \cite{dzh25}. It discusses series expansions of processes with stationary increments (si-processes) and certain associated processes. Making use of de Branges theory of…
The tail measure of a regularly varying stationary time series has been recently introduced. It is used in this contribution to reconsider certain properties of the tail process and establish new ones. A new formulation of the time change…
A new extension of the sub-fractional Brownian motion, and thus of the Brownian motion, is introduced. It is a linear combination of a finite number of sub-fractional Brownian motions, that we have chosen to call the mixed sub-fractional…
We formulate the generalized Sarnak's M\"obius disjointness conjecture for an arbitrary number field $K$, and prove a quantitative disjointness result between polynomial nilsequences $(\Phi(g(n)\Gamma))_{n\in\mathbb{Z}^{D}}$ and aperiodic…
We consider an intersection of past and future property of multivariate stationary processes which is the key to deriving various representation theorems for their linear predictor coefficient matrices. We extend useful spectral…
We study general properties for the family of stochastic processes with polynomial regression property, that is that every conditional moment of the process is a polynomial. It turns out that then there exists a family of polynomial…
We give families of examples where sharp rates of convergence to stationarity of the widely used Gibbs sampler are available. The examples involve standard exponential families and their conjugate priors. In each case, the transition…