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Evolutionarily stable strategies for stochastic processes

Theoretical Population Biology, 2004
The classical definition of evolutionary stability assumes that the fitness of each phenotype is fully determined by the composition of phenotypes in the population and by the strategies of each of these phenotypes. In natural populations, however, stochasticity often plays a crucial role in determining the fitness of an individual and a deterministic ...
Dostálková, Iva, Kindlmann, Pavel
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Extremal stochastic integrals: a parallel between max-stable processes and α-stable processes

Extremes, 2005
The paper is devoted to construction of extremal stochastic integrals by random \(\alpha\)-Fréchet sup-measures and investigation of their properties, specially, connections with \(\alpha\)-stable integrals. A r.v. \(\xi\) has \(\alpha\)-Fréchet distribution \(F(\alpha,\sigma)\) if \(P\{\xi\leq x\}=\exp(-\sigma^\alpha x^{-\alpha})\), \(x>0\).
Stoev, Stilian A., Taqqu, Murad S.
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On one-dimensional stochastic differential equations driven by stable processes

Lithuanian Mathematical Journal, 2000
It is considered the one-dimensional stochastic differential equation \[ X_t= x+ \int^t_0 b(s, X_{s-}) dZ_s,\qquad t\geq 0,\tag{\(*\)} \] where \(Z\) is a symmetry \(\alpha\)-stable Lévy process with \(\alpha\in (1,2]\) and \(b\) is a Borel function.
PRAGARAUSKAS H., ZANZOTTO, Pio Andrea
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Stochastic processes with stable distributions in random environments

Physical Review E, 1996
The asymptotic behavior in random environments of random flights with stable distribution laws is analyzed by the field-theoretic renormalization group. Random force fields with isotropic, divergenceless, curl-free, and unconstrained pair correlation functions with both finite and infinite correlation length are considered.
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Simulation and Chaotic Behaviour of α-Stable Stochastic Processes.

Journal of the Royal Statistical Society. Series A (Statistics in Society), 1995
Preliminary remarks Brownian motion, poisson process, alpha-stable Levy motion computer simulation of alpha-stable random variables stochastic integration spectral representations of stationary processes computer approximations of continuous time processes examples of alpha-stable stochastic modelling convergence of approximate methods chaotic ...
P. M. Lee, A. Janicki, A. Weron
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Some remarks on stable stochastic processes and?-superharmonic functions

Mathematical Notes of the Academy of Sciences of the USSR, 1973
An integral representation is established for a stable multidimensional probability density. It is used for a new and direct proof of the fact that anα-superharmonic function considered on the trajectories of a stable symmetric stochastic process with parameter a is a super-martingale.
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Stable and utility-maximizing scheduling for stochastic processing networks

2009 47th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2009
Stochastic Processing Networks (SPNs) model manufacturing, communication, and service systems. In such a network, service activities require parts and resources to produce other parts. Because service activities compete for resources, a scheduling problem arises.
Libin Jiang, Jean Walrand
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Simulating Stable Stochastic Systems: III. Regenerative Processes and Discrete-Event Simulations

Operations Research, 1975
This paper shows that a previously developed technique for analyzing simulations of GI/G/s queues and Markov chains applies to discrete-event simulations that can be modeled as regenerative processes. It is possible to address questions of simulation run duration and of starting and stopping simulations because of the existence of a random grouping of
Crane, Michael A., Iglehart, Donald L.
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On stochastic processes associated with relativistic stable distributions

Lithuanian Mathematical Journal, 2008
The author considers relativistic \(\alpha\)-stable Lévy processes and proves some distributional properties, like its exact Lévy triplet. Then he constructs the corresponding Ornstein-Uhlenbeck process. Finally he characterizes relativistic \(\alpha\)-stable mixed processes via its transition function an and the local characteristic triplet.
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An efficient algorithm for Levy stable stochastic processes

AIP Conference Proceedings, 1993
We present a new algorithm generating stochastic processes with a probability distribution very close to a Levy stable probability distribution characterized by the parameter α. The parameter α can be selected within the range 0.3≤α≤2. The algorithm is very efficient for 0.75≤α≤1.95.
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