Results 1  10
of
14
Phase Diagram for Turbulent Transport: Sampling Drift, Eddy Diffusivity and Variational Principles
, 2001
"... We study the longtime, large scale transport in a threeparameter family of isotropic, incompressible Gaussian velocity fields with powerlaw spectra. Scaling law for transport is characterized by the scaling exponent q and the Hurst exponent H, as functions of the parameters. The parameter space ..."
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Cited by 7 (6 self)
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We study the longtime, large scale transport in a threeparameter family of isotropic, incompressible Gaussian velocity fields with powerlaw spectra. Scaling law for transport is characterized by the scaling exponent q and the Hurst exponent H, as functions of the parameters. The parameter space is divided into regimes of scaling laws of different functional forms of the scaling exponent and the Hurst exponent. We present the full threedimensional phase diagram. The limiting process is one of three kinds: Brownian motion (H = 1=2), persistent fractional Brownian motions (1=2! H! 1) and regular (or smooth) motion (H = 1). We discover that a critical wave number divides the infrared cutoffs into three categories, critical, subcritical and supercritical; they give rise to different scaling laws. We introduce the notions of sampling drift and eddy diffusivity, and formulate variational principles to estimate the eddy diffusivity. We show that fractional Brownian motions result from a dominant sampling drift.
Diffusion in Turbulence
, 1996
"... We prove long time diffusive behavior (homogenization) for convectiondiffusion in a turbulent that it incompressible and has a stationary and square integrable stream matrix. Simple shear examples show that this result is sharp for flows that have stationary stream matrices. ..."
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Cited by 4 (3 self)
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We prove long time diffusive behavior (homogenization) for convectiondiffusion in a turbulent that it incompressible and has a stationary and square integrable stream matrix. Simple shear examples show that this result is sharp for flows that have stationary stream matrices.
Mathematics of Financial Markets
 in Engquist B., Schmid W., &quot;Mathematics Unlimited  2001 & Beyond&quot;, Springer Berlin 2001
"... Mathematical finance is a child of the 20th century. It was born on 29 March ..."
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Cited by 1 (0 self)
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Mathematical finance is a child of the 20th century. It was born on 29 March
Artificial neural networks as approximators of stochastic processes
 Neural Networks
, 1999
"... Artificial (or biological) Neural Networks must be able to form by learning internal memory of the environment to determine decisions and subsequent actions to stimuli. By assuming that environment is essentially stochastic it follows that the mathematical framework for learning information from env ..."
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Cited by 1 (0 self)
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Artificial (or biological) Neural Networks must be able to form by learning internal memory of the environment to determine decisions and subsequent actions to stimuli. By assuming that environment is essentially stochastic it follows that the mathematical framework for learning information from environment is the theory of stochastic processes approximation. The aim of this paper is to show that classes of neural networks capable of approximating stochastic processes exist. 1
IEEE TRANSACTIONS ON INFORMATION THEORY 1 CrossLayer Design of FDDOFDM Systems based
, 905
"... Abstract — It is wellknown that crosslayer scheduling which adapts power, rate and user allocation can achieve significant gain on system capacity. However, conventional crosslayer designs all require channel state information at the base station (CSIT) which is difficult to obtain in practice. I ..."
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Abstract — It is wellknown that crosslayer scheduling which adapts power, rate and user allocation can achieve significant gain on system capacity. However, conventional crosslayer designs all require channel state information at the base station (CSIT) which is difficult to obtain in practice. In this paper, we focus on crosslayer resource optimization based on ACK/NAK feedback flows in OFDM systems without explicit CSIT. While the problem can be modeled as Markov Decision Process (MDP), brute force approach by policy iteration or value iteration cannot lead to any viable solution. Thus, we derive a simple closedform solution for the MDP crosslayer problem, which is asymptotically optimal for sufficiently small target packet error rate (PER). The proposed solution also has low complexity and is suitable for realtime implementation. It is also shown to achieve significant performance gain compared with systems that do not utilize the ACK/NAK feedbacks for crosslayer designs or crosslayer systems that utilize very unreliable CSIT for adaptation with mismatch in CSIT error statistics. Asymptotic analysis is also provided to obtain useful design insights.
Diffusion in turbulence
, 1994
"... Summary. We prove long time diffusive behavior (homogenization) for convectiondiffusion in a turbulent flow that it incompressible and has a stationary and square integrable stream matrix. Simple shear flow examples show that this result is sharp for flows that have stationary stream matrices. ..."
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Summary. We prove long time diffusive behavior (homogenization) for convectiondiffusion in a turbulent flow that it incompressible and has a stationary and square integrable stream matrix. Simple shear flow examples show that this result is sharp for flows that have stationary stream matrices.