arXiv subjects

O. E. Barndorff-Nielsen

Publications and source records attributed to O. E. Barndorff-Nielsen.

5 recordsLinked to original sources

arXiv2005

A class of spatio-temporal and causal stochastic processes, with application to multiscaling and multifractality

We present a general class of spatio-temporal stochastic processes describing the causal evolution of a positive-valued field in space and time. The field construction is based on independently scattered random measures of Levy type whose weighted amplitudes are integrated within a causality cone. General n-point correlations are derived in closed form. As a special case of the general framework, we consider a causal multiscaling process in space and time in more detail. The latter is derived from, and completely specified by, power-law two-point correlations, and gives rise to scaling behaviour of both purely temporal and spatial higher-order correlations. We further establish the connection to classical multifractality and prove the multifractal nature of the coarse-grained field amplitude.

math-ph↗

arXiv2003

Data-driven derivation of the turbulent energy cascade generator

Within the framework of random multiplicative energy cascade models of fully developed turbulence, expressions for two-point correlators and cumulants are derived, taking into account a proper conversion from an ultrametric to an Euclidean two-point distance. The comparison with two-point statistics of the surrogate energy dissipation, extracted from various wind tunnel and atmospheric boundary layer records, allows an accurate deduction of multiscaling exponents and cumulants. These exponents serve as the input for parametric estimates of the probabilistic cascade generator.

physics.flu-dyn↗

arXiv2003

On Quantum Statistical Inference, II

Interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially, in step with dramatic new developments in experimental techniques for studying small quantum systems. Furthermore, theoretical developments in the theory of quantum measurements have brought the basic mathematical framework for the probability calculations much closer to that of classical probability theory. The present paper reviews this field and proposes and interrelates a number of new concepts for an extension of classical statistical inference to the quantum context.

quant-ph↗

arXiv2003

On Quantum Statistical Inference, I

Recent developments in the mathematical foundations of quantum mechanics have brought the theory closer to that of classical probability and statistics. On the other hand, the unique character of quantum physics sets many of the questions addressed apart from those met classically in stochastics. Furthermore, concurrent advances in experimental techniques and in the theory of quantum computation have led to a strong interest in questions of quantum information, in particular in the sense of the amount of information about unknown parameters in given observational data or accessible through various possible types of measurements. This scenery is outlined (with an audience of statisticians and probabilists in mind).

quant-ph↗

arXiv2000

Fisher information in quantum statistics

Braunstein and Caves (1994) proposed to use Helstrom's {\em quantum information} number to define, meaningfully, a metric on the set of all possible states of a given quantum system. They showed that the quantum information is nothing else than the maximal Fisher information in a measurement of the quantum system, maximized over all possible measurements. Combining this fact with classical statistical results, they argued that the quantum information determines the asymptotically optimal rate at which neighbouring states on some smooth curve can be distinguished, based on arbitrary measurements on $n$ identical copies of the given quantum system. We show that the measurement which maximizes the Fisher information typically depends on the true, unknown, state of the quantum system. We close the resulting loophole in the argument by showing that one can still achieve the same, optimal, rate of distinguishability, by a two stage adaptive measurement procedure. When we consider states lying not on a smooth curve, but on a manifold of higher dimension, the situation becomes much more complex. We show that the notion of ``distinguishability of close-by states'' depends strongly on the measurement resources one allows oneself, and on a further specification of the task at hand. The quantum information matrix no longer seems to play a central role.

quant-ph↗