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19
Representations of Gaussian processes equivalent to Wiener process
 Osaka J. Math
, 1968
"... The purpose of this paper is to get a canonical representation of Gaussian processes which are equivalent (or mutually absolutely continuous) to Wiener process. The main result is this. Suppose we are given a Gaussian process Yt on a probability space (Ω, 33, P), which is equivalent to Wiener proces ..."
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The purpose of this paper is to get a canonical representation of Gaussian processes which are equivalent (or mutually absolutely continuous) to Wiener process. The main result is this. Suppose we are given a Gaussian process Yt on a probability space (Ω, 33, P), which is equivalent to Wiener process. Then
Multisensor Modeling Underwater with Uncertain Information
 Massachusetts Institute of Technology
, 1988
"... Distribution is unlimited 17. DISTRIBUTION STATEMENT (. Off b.tract.ntered I B&let 20. if d11.r,, hem R.p.r) IS. SUPPLEMENTARY NOTES None I. KEY WORDS (Continue n reverse old * it no*eeary md Identlfy y block iember) autonomous robot visual modeling object recognition multisensor fusion navigat ..."
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Cited by 19 (0 self)
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Distribution is unlimited 17. DISTRIBUTION STATEMENT (. Off b.tract.ntered I B&let 20. if d11.r,, hem R.p.r) IS. SUPPLEMENTARY NOTES None I. KEY WORDS (Continue n reverse old * it no*eeary md Identlfy y block iember) autonomous robot visual modeling object recognition multisensor fusion navigation 20. ABSTRACT (Coneinue m revese side It neceery end Idondlfe be, bleck fmmlbr) This thesis develops an approach to the construction of multidimensional stochastic models for intelligent systems exploring an underwater environment. The important characteristics shared by such applications are: realtime constraints: unstructured, threedimensional terrain: highbandwidth sensors providing redundant, overlapping coverage: lack of prior knowledge about the environment: and inherent inaccuracy or ambiguity in sensing and interpretation. The models are cast as a three
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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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 6 (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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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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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
Reinforced Random Walk
"... This thesis aim is to present results on a stochastic model called reinforced random walk. This process was conceived in the late 1980’s by Coppersmith and Diaconis and can be regarded as a generalization of a random walk on a weighted graph. These reinforced walks have nonhomogeneous transition pr ..."
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This thesis aim is to present results on a stochastic model called reinforced random walk. This process was conceived in the late 1980’s by Coppersmith and Diaconis and can be regarded as a generalization of a random walk on a weighted graph. These reinforced walks have nonhomogeneous transition probabilities, which arise from an interaction between the process and the weights. We survey articles on the subject, perform simulations and extend a theorem by Pemantle. Tack Ett stort tack till min handledare Sven Erick Alm för vägledning i matematiken, efterforskningen och inte minst för uppslaget till denna uppsats. Ditt stöd och kunnande gjorde arbetet till en rolig och utvecklande process. Tack ocks˚a till alla som medverkar i utvecklingen av bra och gratis mjukvara, speciellt personerna bakom L ATEX och R. Det förstnämnda programmet typsatte detta arbete och det sistnämnda användes för simuleringarna