We consider stochastic multi-dimensional linear hyperbolic systems of conservation laws. We prove existence and uniqueness of a random weak solution, provide estimates for the regularity of the solution in terms of regularities of input data, and show existence of statistical moments. Bounds for mean square error vs. expected work are proved for the Multi-Level Monte Carlo Finite Volume algorit...

The Schramm-Loewner evolution (SLE) is a one-parameter family of conformally invariant processes that are candidates for scaling limits for two-dimensional lattice models in statistical physics. Analysis of SLE curves requires estimating moments of derivatives of random conformal maps. We show how to use the Girsanov theorem to study the moments for the reverse Loewner flow. As an application, ...

We investigate the almost sure asymptotic properties of vector martingale transforms. Assuming some appropriate regularity conditions both on the increasing process and on the moments of the martingale, we prove that normalized moments of any even order converge in the almost sure central limit theorem for martingales. A conjecture about almost sure upper bounds under wider hypotheses is formul...

In this paper, we consider statistical characteristics of real User Datagram Protocol (UDP) traffic. Four main issues in the study include(i) the presence of long rangedependence (LRD) in the UDP traffic,(ii) the marginal distribution of the UDP traces,(iii) dependence structure of wavelet coefficients,(iv) and performance evaluation of the Hurst parameter estimation based on different numbers ...

A method of EEG analysis is described which provides new insights into EEG pathology in cerebral ischaemia. The method is based on a variant of detrended fluctuation analysis (DFA), which reduces short (10 s) segments of spontaneous EEG time series to two dimensionless scaling exponents. The spatial variability of each exponent is expressed in terms of its statistical moments across EEG channel...

High-Reynolds-number data in turbulent boundary layers are analysed to examine statistical moments of streamwise velocity fluctuations u′. Prior work has shown that the variance of u′ exhibits logarithmic behaviour with distance to the surface, within an inertial sublayer. Here we extend these observations to even-order moments. We show that the 2p-order moments, raised to the power 1/p, also f...

This paper is dedicated to Arthur Krener – a great researcher, a great teacher and a great friend – on the occasion of his 60th birthday. In this work we study the generalized moment problem with complexity constraints in the case where the actual values of the moments are uncertain. For example, in spectral estimation the moments correspond to estimates of covariance lags computed from a finit...

The angular turning probability density distribution for motile bacteria is usually measured in local coordinates and is therefore inconvenient for global analyses of the chemotactic bacterial migration. In this paper we present analytical derivations that convert the local angular turning probability density distribution into a global one. The explicit expression of a reduced global turning pr...

We use a smoothed version of the explicit formula to find an accurate pointwise approximation to the Riemann zeta function as a product over its nontrivial zeros multiplied by a product over the primes. We model the first product by characteristic polynomials of random matrices. This provides a statistical model of the zeta function which involves the primes in a natural way. We then employ the...