LEADER 00913nam--2200337---450- 001 990001558920203316 005 20050831135538.0 035 $a000155892 035 $aUSA01000155892 035 $a(ALEPH)000155892USA01 035 $a000155892 100 $a20040413d1967----km-y0itay0103----ba 101 0 $afre 102 $aFR 105 $a||||||||001yy 200 1 $aElise ou la vrai vie$fClaire Etcherelli 210 $aParis$cDenoel$d1967 215 $a280 p.$d21 cm 410 0$12001 454 1$12001 461 1$1001-------$12001 700 1$aETCHERELLI,$bClaire$0560436 801 0$aIT$bsalbc$gISBD 912 $a990001558920203316 951 $aVI.4. Coll.8/ 21(II F A coll.1/21)$b24613 L.M.$cII F A 959 $aBK 969 $aUMA 979 $aSIAV3$b10$c20040413$lUSA01$h1134 979 $aCOPAT5$b90$c20050831$lUSA01$h1355 996 $aElise ou la vrai vie$9941135 997 $aUNISA LEADER 05187nam 2200601Ia 450 001 9911006785203321 005 20200520144314.0 010 $a1-282-30936-6 010 $a9786612309366 010 $a0-08-091403-9 035 $a(CKB)1000000000789515 035 $a(EBL)472921 035 $a(OCoLC)814418843 035 $a(SSID)ssj0000333936 035 $a(PQKBManifestationID)11242072 035 $a(PQKBTitleCode)TC0000333936 035 $a(PQKBWorkID)10378536 035 $a(PQKB)10039438 035 $a(MiAaPQ)EBC472921 035 $a(EXLCZ)991000000000789515 100 $a20750720d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAdvanced mathematical tools for automatic control engineers$hVolume 2$iStochastic techniques /$fAlexander S. Poznyak 210 $aOxford ;$aAmsterdam $cElsevier$d2009 215 $a1 online resource (568 p.) 300 $aDescription based upon print version of record. 311 $a0-08-044673-6 327 $aFront cover; Half title page; Dedication; Title page; Copyright page; Contents; Preface; Notations and Symbols; List of Figures; List of Tables; PART I: Basics of Probability; Chapter 1. Probability Space; 1.1. Set operations, algebras and sigma-algebras; 1.2. Measurable and probability spaces; 1.3. Borel algebra and probability measures; 1.4. Independence and conditional probability; Chapter 2. Random Variables; 2.1. Measurable functions and random variables; 2.2. Transformation of distributions; 2.3. Continuous random variables; Chapter 3. Mathematical Expectation 327 $a3.1. Definition of mathematical expectation3.2. Calculation of mathematical expectation; 3.3. Covariance, correlation and independence; Chapter 4. Basic Probabilistic Inequalities; 4.1. Moment-type inequalities; 4.2. Probability inequalities for maxima of partial sums; 4.3. Inequalities between moments of sums and summands; Chapter 5. Characteristic Functions; 5.1. Definitions and examples; 5.2. Basic properties of characteristic functions; 5.3. Uniqueness and inversion; PART II: Discrete Time Processes; Chapter 6. Random Sequences; 6.1. Random process in discrete and continuous time 327 $a6.2. Infinitely often events6.3. Properties of Lebesgue integral with probabilistic measure; 6.4. Convergence; Chapter 7. Martingales; 7.1. Conditional expectation relative to a sigma-algebra; 7.2. Martingales and related concepts; 7.3. Main martingale inequalities; 7.4. Convergence; Chapter 8. Limit Theorems as Invariant Laws; 8.1. Characteristics of dependence; 8.2. Law of large numbers; 8.3. Central limit theorem; 8.4. Logarithmic iterative law; PART III: Continuous Time Processes; Chapter 9. Basic Properties of Continuous Time Processes; 9.1. Main definitions; 9.2. Second-order processes 327 $a9.3. Processes with orthogonal and independent incrementsChapter 10. Markov Processes; 10.1. Definition of Markov property; 10.2. Chapman--Kolmogorov equation and transition function; 10.3. Diffusion processes; 10.4. Markov chains; Chapter 11. Stochastic Integrals; 11.1. Time-integral of a sample-path; 11.2. ?-stochastic integrals; 11.3. The Ito? stochastic integral; 11.4. The Stratonovich stochastic integral; Chapter 12. Stochastic Differential Equations; 12.1. Solution as a stochastic process; 12.2. Solutions as diffusion processes; 12.3. Reducing by change of variables 327 $a12.4. Linear stochastic differential equationsPART IV: Applications; Chapter 13. Parametric Identification; 13.1. Introduction; 13.2. Some models of dynamic processes; 13.3. LSM estimating; 13.4. Convergence analysis; 13.5. Information bounds for identification methods; 13.6. Efficient estimates; 13.7. Robustification of identification procedures; Chapter 14. Filtering, Prediction and Smoothing; 14.1. Estimation of random vectors; 14.2. State-estimating of linear discrete-time processes; 14.3. State-estimating of linear continuous-time processes; Chapter 15. Stochastic Approximation 327 $a15.1. Outline of chapter 330 $aThe second volume of this work continues the approach of the first volume, providing mathematical tools for the control engineer and examining such topics as random variables and sequences, iterative logarithmic and large number laws, differential equations, stochastic measurements and optimization, discrete martingales and probability space. It includes proofs of all theorems and contains many examples with solutions.It is written for researchers, engineers and advanced students who wish to increase their familiarity with different topics of modern and classical mathematics related to 606 $aAutomatic control 606 $aEngineering instruments 615 0$aAutomatic control. 615 0$aEngineering instruments. 676 $a510.2462 676 $a629.8312 676 $a629.8312 700 $aPoznyak$b Alexander S$01825463 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911006785203321 996 $aAdvanced mathematical tools for automatic control engineers$94393149 997 $aUNINA