Digital simulation and modeling of nonlinear stochastic systems

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Digitally generated solutions of nonlinear stochastic systems are not unique but depend critically on the numerical integration algorithm used. Some theoretical and practical implications of this dependence are examined. The Ito-Stratonovich controversy concerning the solution of nonlinear stochastic systems is shown to be more than a theoretical debate on maintaining Markov properties as opposed to utilizing the computational rules of ordinary calculus. The theoretical arguments give rise to practical considerations in the formation and solution of discrete models from continuous stochastic systems. Well-known numerical integration algorithms are shown not only to provide different solutions for the same stochastic system but ... continued below

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Pages: 28

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Richardson, J M & Rowland, J R April 1, 1981.

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Description

Digitally generated solutions of nonlinear stochastic systems are not unique but depend critically on the numerical integration algorithm used. Some theoretical and practical implications of this dependence are examined. The Ito-Stratonovich controversy concerning the solution of nonlinear stochastic systems is shown to be more than a theoretical debate on maintaining Markov properties as opposed to utilizing the computational rules of ordinary calculus. The theoretical arguments give rise to practical considerations in the formation and solution of discrete models from continuous stochastic systems. Well-known numerical integration algorithms are shown not only to provide different solutions for the same stochastic system but also to correspond to different stochastic integral definitions. These correspondences are proved by considering first and second moments of solutions that result from different integration algorithms and then comparing the moments to those arising from various stochastic integral definitions. This algorithm-dependence of solutions is in sharp contrast to the deterministic and linear stochastic cases in which unique solutions are determined by any convergent numerical algorithm. Consequences of the relationship between stochastic system solutions and simulation procedures are presented for a nonlinear filtering example. Monte Carlo simulations and statistical tests are applied to the example to illustrate the determining role which computational procedures play in generating solutions.

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Pages: 28

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NTIS, PC A03/MF A01.

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  • Report No.: SAND-80-2080
  • Grant Number: AC04-76DP00789
  • DOI: 10.2172/6489738 | External Link
  • Office of Scientific & Technical Information Report Number: 6489738
  • Archival Resource Key: ark:/67531/metadc1207551

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

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Creation Date

  • April 1, 1981

Added to The UNT Digital Library

  • July 5, 2018, 11:11 p.m.

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  • Aug. 30, 2018, 5:59 p.m.

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Richardson, J M & Rowland, J R. Digital simulation and modeling of nonlinear stochastic systems, report, April 1, 1981; United States. (digital.library.unt.edu/ark:/67531/metadc1207551/: accessed January 22, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.