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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 C. Walrand
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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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Convergence results for tractable inference in α-stable stochastic processes

2017 22nd International Conference on Digital Signal Processing (DSP), 2017
The α-stable distribution is highly intractable for inference because of the lack of a closed form density function in the general case. However, it is well-established that the α-stable distribution admits a Poisson series representation (PSR) in which the terms of the series are a function of the arrival times of a unit rate Poisson process.
Marina Riabiz   +2 more
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COMMENT ON “WEAK CONVERGENCE TO A MATRIX STOCHASTIC INTEGRAL WITH STABLE PROCESSES”

Econometric Theory, 2011
In this comment we identify a lacuna in a proof in the paper by M. Caner published in 1997 in Econometric Theory concerning the weak limit behavior of various expressions involving heavy-tailed multivariate vectors and the convergence of stochastic integrals.
Paulauskas, V.   +2 more
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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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Characterization of stable processes by identically distributed stochastic integrals

Advances in Applied Probability, 1980
Let X ( t ) be a homogeneous and continuous stochastic process with independent increments. The subject of this paper is to characterize the stable process by two identically distributed stochastic integrals formed by means of X( t
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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
Michael A. Crane, Donald L. Iglehart
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Ergodicity of Stochastic Dissipative Equations Driven by α-Stable Process

Stochastic Analysis and Applications, 2013
It is shown that the transition semigroup (P t ) t≥0 corresponding to stochastic dissipative equations driven by α-stable is strong Feller and irreducible for α ∈ (1, 2). This result ensures the ergodicity for the equation.
Xiaobin Sun, Yingchao Xie
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Weak Convergence to a Matrix Stochastic Integral with Stable Processes

Econometric Theory, 1997
This paper generalizes the univariate results of Chan and Tran (1989, Econometric Theory 5, 354–362) and Phillips (1990, Econometric Theory 6, 44–62) to multivariate time series. We develop the limit theory for the least-squares estimate of a VAR(l) for a random walk with independent and identically distributed errors and for I(1) processes with weakly
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