Convergence of random zeros on complex manifolds

We show that the zeros of random sequences of Gaussian systems of polynomials of in- creasing degree almost surely converge to the expected limit distribution under very general hypotheses. In particular,the normalized distribution of zeros of systems of m polynomials of degree N,orthonor- malized on a regular compact set K(?)C~m,almost surely converge to the equilibrium measure on K as N→∞.     

Path properties of l_p-valued Gaussian random fields

General limit theorems are established for l~p-valued Gaussian random fields indexed by a multidimensional parameter,which contain both almost sure moduli of continuity and limits of large increments for the l~p-valued Gaussian random fields under(?)explicit conditions.     

Convergence of scaled vector fields and local approximation theorem on Carnot-Carathéodory spaces and applications

Doklady Mathematics -     

Distribution of the supremum of random processes from quasi-BanachK σ-spaces

We study random processes from quasi-BanachK _σ-spaces of random variables whose domain of definition is not necessarily a compact set. We establish conditions under which the supremum of a properly normalized process belongs to the same space as the process itself. We also obtain estimates for the norm of this supremum. Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 7, pp. 918–930, July, 1999.     

Passage times of random walks and Lévy processes across power law boundaries

We establish an integral test involving only the distribution of the increments of a random walk S which determines whether limsup _n→∞(S_n/n^κ) is almost surely zero, finite or infinite when 1/2<κ<1 and a typical step in the random walk has zero mean. This completes the results of Kesten and Maller [9] concerning finiteness of one-sided passage times over power law boundaries, so that we now have quite explicit criteria for all values of κ≥0. The results, and those of [9], are also extended to Lévy processes.This work is partially supported by ARC Grant DP0210572.     

Pointwise Convergence and Uniform Convergence of Wavelet Frame Series

Pointwise convergence and uniform convergence for wavelet frame series is a new topic. With the help of band-limited dual wavelet frames, this topic is first researched.     

Conditional random fields for entity extraction and ontological text coding

Previous research suggests that one field with a strong yet unsatisfied need for automatically extracting instances of various entity classes from texts is the analysis of socio-technical systems (Feldstein in Media in Transition MiT5, 2007; Hampe et al. in Netzwerkanalyse und Netzwerktheorie, 2007; Weil et al. in Proceedings of the 2006 Command and Control Research and Technology Symposium, 2006; Diesner and Carley in XXV Sunbelt Social Network Conference, 2005). Traditional as well as non-traditional and customized sets of entity classes and the relationships between them are often specified in ontologies or taxonomies. We present a Conditional Random Fields (CRF)-based approach to distilling a set of entities that are defined in an ontology originating from organization science. CRF, a supervised sequential machine learning technique, facilitates the derivation of relational data from corpora by locating and classifying instances of various entity classes. The classified entities can be used as nodes for the construction of socio-technical networks. We find the outcome sufficiently accurate (82.7 percent accuracy of locating and classifying entities) for future application in the described problem domain. We propose using the presented methodology as a crucial step in the process of advanced modeling and analysis of complex and dynamic networks.

On convergence of random walks generated by compound Cox processes to Lévy processes

A functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes to Lévy processes in the Skorokhod space. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with mixed normal distributions, and in particular, to stable Lévy processes.     

Moderate deviations and functional limits for random processes with stationary and independent increments

We first give a functional moderate deviation principle for random processes with stationary and independent increments under the Ledoux's condition. Then we apply the result to the functional limits for increments of the processes and obtain some Csorgo-Revesz type functional laws of the iterated logarithm.     

“Poisson” models of random fields with applications in transport theory

A comparative analysis of various models of exponentially correlated random fields associated with Poisson point ensembles is given. Algorithms for the modeling of radiative transfer in random media of this type are considered. An asymptotic estimate for the particle passage probability is constructed assuming that the flow of trajectory intersections with domains of constant random density is Poisson distributed.     

δ - and δ ′-shocks and the transportation and concentration processes

Using the definitions of δ - and δ ′-shocks for some systems of conservation laws, the corresponding Rankine–Hugoniot conditions are derived. We also derive the balance laws describing area, volume, mass and momentum transportation between the area outside the wave front and the wave front. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Kahane–Khintchine inequalities and functional central limit theorem for stationary random fields

We establish new Kahane–Khintchine inequalities in Orlicz spaces induced by exponential Young functions for stationary real random fields which are bounded or satisfy some finite exponential moment condition. Next, we give sufficient conditions for partial sum processes indexed by classes of sets satisfying some metric entropy condition to converge in distribution to a set-indexed Brownian motion. Moreover, the class of random fields that we study includes φ-mixing and martingale difference random fields.     

Chung’s law of the iterated logarithm for anisotropic Gaussian random fields

In this paper we establish Chung’s law of the iterated logarithm for a class of anisotropic Gaussian random fields with stationary increments. This result is applicable to space–time Gaussian random fields and solution to the stochastic fractional heat equation.     

Convergence in distribution of random metric measure spaces (Λ-coalescent measure trees)

We consider the space of complete and separable metric spaces which are equipped with a probability measure. A notion of convergence is given based on the philosophy that a sequence of metric measure spaces converges if and only if all finite subspaces sampled from these spaces converge. This topology is metrized following Gromov’s idea of embedding two metric spaces isometrically into a common metric space combined with the Prohorov metric between probability measures on a fixed metric space. We show that for this topology convergence in distribution follows—provided the sequence is tight—from convergence of all randomly sampled finite subspaces. We give a characterization of tightness based on quantities which are reasonably easy to calculate. Subspaces of particular interest are the space of real trees and of ultra-metric spaces equipped with a probability measure. As an example we characterize convergence in distribution for the (ultra-)metric measure spaces given by the random genealogies of the Λ-coalescents. We show that the Λ-coalescent defines an infinite (random) metric measure space if and only if the so-called “dust-free”-property holds.     

Controlled random fields,von Neumann–Gale dynamics and multimarket hedging with risk

We develop a model of asset pricing and hedging for interconnected financial markets with frictions – transaction costs and portfolio constraints. The model is based on a control theory for random fields on a directed graph. Market dynamics are described by using von Neumann–Gale dynamical systems first considered in connection with the modelling of economic growth [13,24]. The main results are hedging criteria stated in terms of risk-acceptable portfolios and consistent price systems, extending the classical superreplication criteria formulated in terms of equivalent martingale measures.     

Moduli of continuity for <Emphasis Type="Italic">l</Emphasis><Superscript>∞</Superscript>-valued Gaussian random fields

This paper establishes the general moduli of continuity for l ^∞-valued Gaussian random fields {X(t):= (X ₁(t),X ₂(t), h.), t ∈ [0, ∞) ^N } indexed by the N-dimensional parameter t:= (t ₁,…,t _N ), under the explicit condition yielding that the covariance function of distinct increments of X _k (t) for fixed k ≧ 1 is positive or nonpositive. Supported by KOSEF-R01-2008-000-11418-0.     

Langevin equations for L′-Valued Gaussian processes and fluctuation limits of infinite particle systems

Summary L Gaussian processes of a certain class are shown to satisfy generalized Langevin equations. Examples are fluctuation limits of several infinite particle systems, in particular infinite particle branching Brownian motions with immigration under various scalings and the voter model with hydrodynamic scaling.Partially supported by CONACyT grants PCCBBNA 002042 and 140102 G203-006 (México) and a grant of the NSERC (Canada)