| Description |
1 online resource (261 p.) |
| Contents |
Cover -- Title Page -- Copyright Page -- Contents -- Preface -- Introduction -- Chapter 1. Multidimensional Models of Kac Type -- 1.1.Definitions and basic properties -- 1.2.Moments of evolutionary process -- 1.3. Systems of Kolmogorov equations -- 1.4. Evolutionary operator and theorem about weak convergence to themeasure of theWiener process -- Chapter 2. Symmetry of Markov Random Evolutionary Processes in Rn -- 2.1. Symmetrization: definition and properties -- 2.2. Examples of symmetric distributions in Rn and distributions on n + 1-hedra -- 2.2.1. Symmetricdistributions |
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2.2.2. Distributions on n + 1-hedra -- Chapter 3. Hyperparabolic Equations, Integral Equation and Distribution for Markov Random Evolutionary Processes -- 3.1. Hyperparabolic equations and methods of solving Cauchy problems -- 3.2. Analytical solution of a hyperparabolic equation with real-analytic initial conditions -- 3.3. Integral representation of the hyperparabolic equation -- 3.4.Distributionfunction of evolutionary process -- Chapter 4. Fading Markov Random Evolutionary Process -- 4.1. Definition of fading Markov random evolutionary process, its moments and limit distribution |
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4.2. Integral equation for a function from the fading random evolutionary process -- 4.3. Equations in partial derivatives for a function of the fading random evolutionary process -- Chapter 5. Two Models of the Evolutionary Process -- 5.1.Evolution on a complex plane -- 5.2.Evolutionwithinfinitelymany directions -- 5.2.1. Symmetric case -- 5.2.2.Non-symmetric case -- Chapter 6. Diffusion Process with Evolution and Its Parameter Estimation -- 6.1.Asymptotic diffusion environment -- 6.2. Approximation of a discrete Markov process in asymptotic diffusion environment |
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6.3. Parameter estimation of the limit process -- Chapter 7. Filtration of Stationary Gaussian Statistical Experiments -- 7.1. Introduction -- 7.2. Stochastic difference equation of the process of filtration -- 7.3.Coefficient of filtration -- 7.4.Equation of optimal filtration -- 7.5.Characterization of afilteredsignal -- Chapter 8. Adapted Statistical Experiments with Random Change of Time -- 8.1. Introduction -- 8.2. Statistical experiments and evolutionary processes -- 8.3. Stochastic dynamics of statistical experiments -- 8.4.Adapted statistical experiments in series scheme |
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8.5.Convergence of the adapted statistical experiments -- 8.6. Scaling parameter estimation -- 8.7. Statistical estimations of the renewal intensity parameter -- 8.7.1. Poisson's renewal process with parameter q = 2 -- 8.7.2. Stationary renewal process with delay, determined by the initial distribution function of the limit overjumps -- 8.7.3.Renewal processeswith arbitrarilydistributed renewal intervals -- Chapter 9. Filtering of Stationary Gaussian Statistical Experiments -- 9.1. Stationary statistical experiments -- 9.2. Filtering of discrete Markov diffusion -- 9.3.Thefilteringerror |
| Notes |
Description based upon print version of record |
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9.4.Thefilteringempirical estimation |
| Form |
Electronic book
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| Author |
Samoilenko, Igor
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| ISBN |
9781394229468 |
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1394229461 |
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1394229488 |
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9781394229482 |
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