For many natural turbulent dynamic systems, observed high dimensional dynamic data can be approximated at slow time scales by a process Xt driven by a systems of stochastic differential equations (SDEs). When one tries to estimate the parameters of this unobservable SDEs systems, there is a clear mismatch between the available data and the SDEs dynamics to be parametrized. Here, we formalize th...

We study dynamical reversibility in stationary stochastic processes from an information-theoretic perspective. Extending earlier work on the reversibility of Markov chains, we focus on finitary processes with arbitrarily long conditional correlations. In particular, we examine stationary processes represented or generated by edge-emitting, finite-state hidden Markov models. Surprisingly, we fin...

It has recently been proposed that phenotypic variation in clonal populations of bacterial species results from intracellular "noise," i.e., random fluctuations in levels of cellular molecules, which would be predicted to be insensitive to selective pressure. To test this notion, we propagated five populations of Bacillus subtilis for 5,000 generations with selection for one phenotype: the deci...

We consider a random surface in R d tesselating the space into cells and a random vector eld u which is smooth on each cell but may jump on. Assuming the pair ((; u) stationary we prove an inversion formula expressing the probability of an event under the stationary probability in terms of the Palm probability P deened by the random surface measure associated with. This result involves the ow o...

Stationary quantum stochastic process j is introduced as a *homomorphism embedding an involutive graded algebra K̃ = ⊕i=1Ki into a ring of (abelian) cohomologies of the one-parameter group α consisting of *-automorphisms of certain operator algebra in a Hilbert space such that every x from Ki is translated into an additive i− αcocycle j(x). It is shown that (noncommutative) multiplicative markov...

This letter investigates the supervised learning problem with observations drawn from certain general stationary stochastic processes. Here by general, we mean that many stationary stochastic processes can be included. We show that when the stochastic processes satisfy a generalized Bernstein-type inequality, a unified treatment on analyzing the learning schemes with various mixing processes ca...

Time series in many areas of application often display local or global trends. Typical models that provide statistical \explanations" of such trends are, for example, polynomial regression, smooth bounded trends that are estimated nonparametrically, and di erence-stationary processes such as, for instance, integrated ARIMA processes. In addition, there is a fast growing literature on stationary...

We introduce a concept of a quantum wide sense stationary process taking values in a C*-algebra and expected in a sub-algebra. The power spectrum of such a process is defined, in analogy to classical theory, as a positive measure on frequency space taking values in the expected algebra. The notion of linear quantum filters is introduced as some simple examples mentioned. 1 Spectral Analysis of ...

A validated simulation model primarily requires performing an appropriate input analysis mainly by determining the behavior of real-world processes using probability distributions. In many practical cases, probability distributions of the random inputs vary over time in such a way that the functional forms of the distributions and/or their parameters depend on time. This paper answers the quest...

We examine the auto-dependence structure of strictly stationary solutions of linear stochastic recurrence equations and of strictly stationary GARCH(1, 1) processes from the point of view of ordinary and generalized tail dependence coefficients. Since such processes can easily be of infinite variance, a substitute for the usual auto-correlation function is needed. Mathematics Subject Classifica...