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Random Elements (random + element)

Distribution by Scientific Domains

Mathematics and Statistics	57%

Selected Abstracts

ON THE STRONG LAW OF LARGE NUMBERS UNDER REARRANGEMENTS FOR SEQUENCES OF BLOCKWISE ORTHOGONAL RANDOM ELEMENTS IN BANACH SPACES

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 4 2007
Nguyen Van Quang
Summary The condition of the strong law of large numbers is obtained for sequences of random elements in type p Banach spaces that are blockwise orthogonal. The current work extends a result of Chobanyan & Mandrekar (2000)[On Kolmogorov SLLN under rearrangements for orthogonal random variables in a B -space. J. Theoret. Probab. 13, 135,139.] Special cases of the main results are presented as corollaries, and illustrative examples are provided. [source]

Linear random vibration by stochastic reduced-order models

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2010
Mircea Grigoriu
Abstract A practical method is developed for calculating statistics of the states of linear dynamic systems with deterministic properties subjected to non-Gaussian noise and systems with uncertain properties subjected to Gaussian and non-Gaussian noise. These classes of problems are relevant as most systems have uncertain properties, physical noise is rarely Gaussian, and the classical theory of linear random vibration applies to deterministic systems and can only deliver the first two moments of a system state if the noise is non-Gaussian. The method (1) is based on approximate representations of all or some of the random elements in the definition of linear random vibration problems by stochastic reduced-order models (SROMs), that is, simple random elements having a finite number of outcomes of unequal probabilities, (2) can be used to calculate statistics of a system state beyond its first two moments, and (3) establishes bounds on the discrepancy between exact and SROM-based solutions of linear random vibration problems. The implementation of the method has required to integrate existing and new numerical algorithms. Examples are presented to illustrate the application of the proposed method and assess its accuracy. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Linking movement behaviour, dispersal and population processes: is individual variation a key?

JOURNAL OF ANIMAL ECOLOGY, Issue 5 2009
Colin Hawkes
Summary 1Movement behaviour has become increasingly important in dispersal ecology and dispersal is central to the development of spatially explicit population ecology. The ways in which the elements have been brought together are reviewed with particular emphasis on dispersal distance distributions and the value of mechanistic models. 2There is a continuous range of movement behaviours and in some species, dispersal is a clearly delineated event but not in others. The biological complexities restrict conclusions to high-level generalizations but there may be principles that are common to dispersal and other movements. 3Random walk and diffusion models when appropriately elaborated can provide an understanding of dispersal distance relationships on spatial and temporal scales relevant to dispersal. Leptokurtosis in the relationships may be the result of a combination of factors including population heterogeneity, correlation, landscape features, time integration and density dependence. The inclusion in diffusion models of individual variation appears to be a useful elaboration. The limitations of the negative exponential and other phenomenological models are discussed. 4The dynamics of metapopulation models are sensitive to what appears to be small differences in the assumptions about dispersal. In order to represent dispersal realistically in population models, it is suggested that phenomenological models should be replaced by those based on movement behaviour incorporating individual variation. 5The conclusions are presented as a set of candidate principles for evaluation. The main features of the principles are that uncorrelated or correlated random walk, not linear movement, is expected where the directions of habitat patches are unpredictable and more complex behaviour when organisms have the ability to orientate or navigate. Individuals within populations vary in their movement behaviour and dispersal; part of this variation is a product of random elements in movement behaviour and some of it is heritable. Local and metapopulation dynamics are influenced by population heterogeneity in dispersal characteristics and heritable changes in dispersal propensity occur on time-scales short enough to impact population dynamics. [source]

Generating random elements of abelian groups

RANDOM STRUCTURES AND ALGORITHMS, Issue 4 2005
András Lukács
Algorithms based on rapidly mixing Markov chains are discussed to produce nearly uniformly distributed random elements in abelian groups of finite order. Let A be an abelian group generated by set S. Then one can generate ,-nearly uniform random elements of A using 4|S|log(|A|/,) log(|A|) additions and the same number of random bits. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005 [source]