Stochastic systems /:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York :
Academic Press,
1983.
|
| Series: | Mathematics in science and engineering ;
v. 169. |
| Subjects: | |
| Online Access: | DE-862 DE-863 DE-862 DE-863 |
| Physical Description: | 1 online resource (xvii, 331 pages) |
| Format: | Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9780080956756 0080956750 1282290339 9781282290334 0120443708 9780120443703 9786612290336 6612290331 |
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| 245 | 1 | 0 | |a Stochastic systems / |c George Adomian. |
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| 490 | 1 | |a Mathematics in science and engineering ; |v v. 169 | |
| 504 | |a Includes bibliographical references and index. | ||
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| 505 | 0 | |a Front Cover; Stochastic Systems; Copyright Page; Contents; Foreword; Preface; Chapter 1. Green's Functions and Systems Theory; 1.1. Introduction: Some Remarks on the Mathematical Modeling of Dynamical Systems; 1.2. Linearity and Superposition; 1.3. The Concept of a Green's Function; 1.4. Simple Input-Output Systems and Green's Functions; 1.5. Operator Forms; 1.6. Green's Function for the Inhomogeneous Sturm-Liouville Operator; 1.7. Properties of the Green's Function; 1.8. Evaluation of the Wronskian; 1.9. Solution Using Abel's Formula | |
| 505 | 8 | |a 1.10. Use of Green's Function to Solve the Inhomogeneous Equation1.11. Adjoint Operators; 1.12. Green's Functions for Adjoint Operators; 1.13. Symbolic Functions; 1.14. Sturm-Liouville Differential Equation; 1.15. Boundary Conditions Specified on a Finite Interval [a, b]; 1.16. Series Expansions for G(x,?); 1.17. Multiple-Input-Multiple-Output Systems; 1.18. Bilinear Form of the Green's Function; 1.19. Bilinear Form of the Green's Function for the Sturm-Liouville Differential Equation; 1.20. Cases Where the Green's Function Does Not Exist; 1.21. Multidimensional Green's Functions | |
| 505 | 8 | |a 1.22. Green's Functions for Initial Conditions1.23. Approximate Calculation of Green's Functions; References; Chapter 2. A Basic Review of the Theory of Stochastic Processes; 2.1. The Nature of a Stochastic Process; 2.2. Stochastic Processes-Basic Definitions; 2.3. Characterization and Classification of Stochastic Processes; 2.4. Consistency Conditions on the Distribution; 2.5. Some Simple Stochastic Processes; 2.6. Time Dependences of Distributions; 2.7. Statistical Measures of Stochastic Processes; 2.8. Random Fields; 2.9. The Calculus of Stochastic Processes | |
| 505 | 8 | |a 2.10. Expansions of Random Functions2.11. Ergodic Theorems; 2.12. Generalized Random Processes; References; Chapter 3. Stochastic Operators and Stochastic Systems; 3.1. Stochastic Systems-Basic Concepts; 3.2. Stochastic Green's Functions; 3.3. Statistical Operators; 3.4. Stochastic Green's Theorem; 3.5. Determination of the Kernel from the Physical Process; References; Chapter 4. Linear Stochastic Differential Equations; 4.1. Stochastic Differential Operators; 4.2. The Differential Equation Formulation; 4.3. Derivation of Stochastic Green's Theorem; 4.4. Hierarchy or Averaging Method | |
| 505 | 8 | |a 4.5. Perturbation Theory4.6. Connection between Perturbation Theory and the Hierarchy Method; 4.7. The Decomposition Method; 4.8. Differential Operator with One Random Coefficient; 4.9. A Convenient Resolvent Kernel Formulation; 4.10. Inverse Operator Form of the Decomposition Method Solution; 4.11. Some Further Remarks on the Operator Identity (4.10.1); 4.12. General Form of the Stochastic Green's Function; 4.13. Random Initial Conditions; 4.14. Simplifying Green's Function Calculations for Higher Order Equations; References; Chapter 5. Nonlinear Stochastic Differential Equations | |
| 546 | |a English. | ||
| 650 | 0 | |a Stochastic differential equations. |0 http://id.loc.gov/authorities/subjects/sh85128177 | |
| 650 | 0 | |a Stochastic systems. |0 http://id.loc.gov/authorities/subjects/sh85128185 | |
| 650 | 6 | |a Équations différentielles stochastiques. | |
| 650 | 6 | |a Systèmes stochastiques. | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x General. |2 bisacsh | |
| 650 | 7 | |a Stochastic differential equations |2 fast | |
| 650 | 7 | |a Stochastic systems |2 fast | |
| 650 | 7 | |a Stochastische Differentialgleichung |2 gnd | |
| 650 | 7 | |a Stochastisches System |2 gnd |0 http://d-nb.info/gnd/4057635-8 | |
| 758 | |i has work: |a Stochastic systems (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGTyBbdvXCKjCtF7kbdjT3 |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
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Record in the Search Index
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| author | Adomian, G. |
| author_GND | http://id.loc.gov/authorities/names/n80091498 |
| author_facet | Adomian, G. |
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| contents | Front Cover; Stochastic Systems; Copyright Page; Contents; Foreword; Preface; Chapter 1. Green's Functions and Systems Theory; 1.1. Introduction: Some Remarks on the Mathematical Modeling of Dynamical Systems; 1.2. Linearity and Superposition; 1.3. The Concept of a Green's Function; 1.4. Simple Input-Output Systems and Green's Functions; 1.5. Operator Forms; 1.6. Green's Function for the Inhomogeneous Sturm-Liouville Operator; 1.7. Properties of the Green's Function; 1.8. Evaluation of the Wronskian; 1.9. Solution Using Abel's Formula 1.10. Use of Green's Function to Solve the Inhomogeneous Equation1.11. Adjoint Operators; 1.12. Green's Functions for Adjoint Operators; 1.13. Symbolic Functions; 1.14. Sturm-Liouville Differential Equation; 1.15. Boundary Conditions Specified on a Finite Interval [a, b]; 1.16. Series Expansions for G(x,?); 1.17. Multiple-Input-Multiple-Output Systems; 1.18. Bilinear Form of the Green's Function; 1.19. Bilinear Form of the Green's Function for the Sturm-Liouville Differential Equation; 1.20. Cases Where the Green's Function Does Not Exist; 1.21. Multidimensional Green's Functions 1.22. Green's Functions for Initial Conditions1.23. Approximate Calculation of Green's Functions; References; Chapter 2. A Basic Review of the Theory of Stochastic Processes; 2.1. The Nature of a Stochastic Process; 2.2. Stochastic Processes-Basic Definitions; 2.3. Characterization and Classification of Stochastic Processes; 2.4. Consistency Conditions on the Distribution; 2.5. Some Simple Stochastic Processes; 2.6. Time Dependences of Distributions; 2.7. Statistical Measures of Stochastic Processes; 2.8. Random Fields; 2.9. The Calculus of Stochastic Processes 2.10. Expansions of Random Functions2.11. Ergodic Theorems; 2.12. Generalized Random Processes; References; Chapter 3. Stochastic Operators and Stochastic Systems; 3.1. Stochastic Systems-Basic Concepts; 3.2. Stochastic Green's Functions; 3.3. Statistical Operators; 3.4. Stochastic Green's Theorem; 3.5. Determination of the Kernel from the Physical Process; References; Chapter 4. Linear Stochastic Differential Equations; 4.1. Stochastic Differential Operators; 4.2. The Differential Equation Formulation; 4.3. Derivation of Stochastic Green's Theorem; 4.4. Hierarchy or Averaging Method 4.5. Perturbation Theory4.6. Connection between Perturbation Theory and the Hierarchy Method; 4.7. The Decomposition Method; 4.8. Differential Operator with One Random Coefficient; 4.9. A Convenient Resolvent Kernel Formulation; 4.10. Inverse Operator Form of the Decomposition Method Solution; 4.11. Some Further Remarks on the Operator Identity (4.10.1); 4.12. General Form of the Stochastic Green's Function; 4.13. Random Initial Conditions; 4.14. Simplifying Green's Function Calculations for Higher Order Equations; References; Chapter 5. Nonlinear Stochastic Differential Equations |
| ctrlnum | (OCoLC)316564070 |
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| id | ZDB-4-EBA-ocn316564070 |
| illustrated | Not Illustrated |
| indexdate | 2025-04-11T08:36:20Z |
| institution | BVB |
| isbn | 9780080956756 0080956750 1282290339 9781282290334 0120443708 9780120443703 9786612290336 6612290331 |
| language | English |
| oclc_num | 316564070 |
| open_access_boolean | |
| owner | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| physical | 1 online resource (xvii, 331 pages) |
| psigel | ZDB-4-EBA FWS_PDA_EBA ZDB-4-EBA |
| publishDate | 1983 |
| publishDateSearch | 1983 |
| publishDateSort | 1983 |
| publisher | Academic Press, |
| record_format | marc |
| series | Mathematics in science and engineering ; |
| series2 | Mathematics in science and engineering ; |
| spelling | Adomian, G. http://id.loc.gov/authorities/names/n80091498 Stochastic systems / George Adomian. New York : Academic Press, 1983. 1 online resource (xvii, 331 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Mathematics in science and engineering ; v. 169 Includes bibliographical references and index. Print version record. Use copy Restrictions unspecified star MiAaHDL Electronic reproduction. [Place of publication not identified] : HathiTrust Digital Library, 2010. MiAaHDL Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL Front Cover; Stochastic Systems; Copyright Page; Contents; Foreword; Preface; Chapter 1. Green's Functions and Systems Theory; 1.1. Introduction: Some Remarks on the Mathematical Modeling of Dynamical Systems; 1.2. Linearity and Superposition; 1.3. The Concept of a Green's Function; 1.4. Simple Input-Output Systems and Green's Functions; 1.5. Operator Forms; 1.6. Green's Function for the Inhomogeneous Sturm-Liouville Operator; 1.7. Properties of the Green's Function; 1.8. Evaluation of the Wronskian; 1.9. Solution Using Abel's Formula 1.10. Use of Green's Function to Solve the Inhomogeneous Equation1.11. Adjoint Operators; 1.12. Green's Functions for Adjoint Operators; 1.13. Symbolic Functions; 1.14. Sturm-Liouville Differential Equation; 1.15. Boundary Conditions Specified on a Finite Interval [a, b]; 1.16. Series Expansions for G(x,?); 1.17. Multiple-Input-Multiple-Output Systems; 1.18. Bilinear Form of the Green's Function; 1.19. Bilinear Form of the Green's Function for the Sturm-Liouville Differential Equation; 1.20. Cases Where the Green's Function Does Not Exist; 1.21. Multidimensional Green's Functions 1.22. Green's Functions for Initial Conditions1.23. Approximate Calculation of Green's Functions; References; Chapter 2. A Basic Review of the Theory of Stochastic Processes; 2.1. The Nature of a Stochastic Process; 2.2. Stochastic Processes-Basic Definitions; 2.3. Characterization and Classification of Stochastic Processes; 2.4. Consistency Conditions on the Distribution; 2.5. Some Simple Stochastic Processes; 2.6. Time Dependences of Distributions; 2.7. Statistical Measures of Stochastic Processes; 2.8. Random Fields; 2.9. The Calculus of Stochastic Processes 2.10. Expansions of Random Functions2.11. Ergodic Theorems; 2.12. Generalized Random Processes; References; Chapter 3. Stochastic Operators and Stochastic Systems; 3.1. Stochastic Systems-Basic Concepts; 3.2. Stochastic Green's Functions; 3.3. Statistical Operators; 3.4. Stochastic Green's Theorem; 3.5. Determination of the Kernel from the Physical Process; References; Chapter 4. Linear Stochastic Differential Equations; 4.1. Stochastic Differential Operators; 4.2. The Differential Equation Formulation; 4.3. Derivation of Stochastic Green's Theorem; 4.4. Hierarchy or Averaging Method 4.5. Perturbation Theory4.6. Connection between Perturbation Theory and the Hierarchy Method; 4.7. The Decomposition Method; 4.8. Differential Operator with One Random Coefficient; 4.9. A Convenient Resolvent Kernel Formulation; 4.10. Inverse Operator Form of the Decomposition Method Solution; 4.11. Some Further Remarks on the Operator Identity (4.10.1); 4.12. General Form of the Stochastic Green's Function; 4.13. Random Initial Conditions; 4.14. Simplifying Green's Function Calculations for Higher Order Equations; References; Chapter 5. Nonlinear Stochastic Differential Equations English. Stochastic differential equations. http://id.loc.gov/authorities/subjects/sh85128177 Stochastic systems. http://id.loc.gov/authorities/subjects/sh85128185 Équations différentielles stochastiques. Systèmes stochastiques. MATHEMATICS Probability & Statistics General. bisacsh Stochastic differential equations fast Stochastic systems fast Stochastische Differentialgleichung gnd Stochastisches System gnd http://d-nb.info/gnd/4057635-8 has work: Stochastic systems (Text) https://id.oclc.org/worldcat/entity/E39PCGTyBbdvXCKjCtF7kbdjT3 https://id.oclc.org/worldcat/ontology/hasWork Print version: Adomian, G. Stochastic systems. New York : Academic Press, ©1983 9780120443703 (DLC) 82016392 (OCoLC)8786046 Mathematics in science and engineering ; v. 169. http://id.loc.gov/authorities/names/n42015986 |
| spellingShingle | Adomian, G. Stochastic systems / Mathematics in science and engineering ; Front Cover; Stochastic Systems; Copyright Page; Contents; Foreword; Preface; Chapter 1. Green's Functions and Systems Theory; 1.1. Introduction: Some Remarks on the Mathematical Modeling of Dynamical Systems; 1.2. Linearity and Superposition; 1.3. The Concept of a Green's Function; 1.4. Simple Input-Output Systems and Green's Functions; 1.5. Operator Forms; 1.6. Green's Function for the Inhomogeneous Sturm-Liouville Operator; 1.7. Properties of the Green's Function; 1.8. Evaluation of the Wronskian; 1.9. Solution Using Abel's Formula 1.10. Use of Green's Function to Solve the Inhomogeneous Equation1.11. Adjoint Operators; 1.12. Green's Functions for Adjoint Operators; 1.13. Symbolic Functions; 1.14. Sturm-Liouville Differential Equation; 1.15. Boundary Conditions Specified on a Finite Interval [a, b]; 1.16. Series Expansions for G(x,?); 1.17. Multiple-Input-Multiple-Output Systems; 1.18. Bilinear Form of the Green's Function; 1.19. Bilinear Form of the Green's Function for the Sturm-Liouville Differential Equation; 1.20. Cases Where the Green's Function Does Not Exist; 1.21. Multidimensional Green's Functions 1.22. Green's Functions for Initial Conditions1.23. Approximate Calculation of Green's Functions; References; Chapter 2. A Basic Review of the Theory of Stochastic Processes; 2.1. The Nature of a Stochastic Process; 2.2. Stochastic Processes-Basic Definitions; 2.3. Characterization and Classification of Stochastic Processes; 2.4. Consistency Conditions on the Distribution; 2.5. Some Simple Stochastic Processes; 2.6. Time Dependences of Distributions; 2.7. Statistical Measures of Stochastic Processes; 2.8. Random Fields; 2.9. The Calculus of Stochastic Processes 2.10. Expansions of Random Functions2.11. Ergodic Theorems; 2.12. Generalized Random Processes; References; Chapter 3. Stochastic Operators and Stochastic Systems; 3.1. Stochastic Systems-Basic Concepts; 3.2. Stochastic Green's Functions; 3.3. Statistical Operators; 3.4. Stochastic Green's Theorem; 3.5. Determination of the Kernel from the Physical Process; References; Chapter 4. Linear Stochastic Differential Equations; 4.1. Stochastic Differential Operators; 4.2. The Differential Equation Formulation; 4.3. Derivation of Stochastic Green's Theorem; 4.4. Hierarchy or Averaging Method 4.5. Perturbation Theory4.6. Connection between Perturbation Theory and the Hierarchy Method; 4.7. The Decomposition Method; 4.8. Differential Operator with One Random Coefficient; 4.9. A Convenient Resolvent Kernel Formulation; 4.10. Inverse Operator Form of the Decomposition Method Solution; 4.11. Some Further Remarks on the Operator Identity (4.10.1); 4.12. General Form of the Stochastic Green's Function; 4.13. Random Initial Conditions; 4.14. Simplifying Green's Function Calculations for Higher Order Equations; References; Chapter 5. Nonlinear Stochastic Differential Equations Stochastic differential equations. http://id.loc.gov/authorities/subjects/sh85128177 Stochastic systems. http://id.loc.gov/authorities/subjects/sh85128185 Équations différentielles stochastiques. Systèmes stochastiques. MATHEMATICS Probability & Statistics General. bisacsh Stochastic differential equations fast Stochastic systems fast Stochastische Differentialgleichung gnd Stochastisches System gnd http://d-nb.info/gnd/4057635-8 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85128177 http://id.loc.gov/authorities/subjects/sh85128185 http://d-nb.info/gnd/4057635-8 |
| title | Stochastic systems / |
| title_auth | Stochastic systems / |
| title_exact_search | Stochastic systems / |
| title_full | Stochastic systems / George Adomian. |
| title_fullStr | Stochastic systems / George Adomian. |
| title_full_unstemmed | Stochastic systems / George Adomian. |
| title_short | Stochastic systems / |
| title_sort | stochastic systems |
| topic | Stochastic differential equations. http://id.loc.gov/authorities/subjects/sh85128177 Stochastic systems. http://id.loc.gov/authorities/subjects/sh85128185 Équations différentielles stochastiques. Systèmes stochastiques. MATHEMATICS Probability & Statistics General. bisacsh Stochastic differential equations fast Stochastic systems fast Stochastische Differentialgleichung gnd Stochastisches System gnd http://d-nb.info/gnd/4057635-8 |
| topic_facet | Stochastic differential equations. Stochastic systems. Équations différentielles stochastiques. Systèmes stochastiques. MATHEMATICS Probability & Statistics General. Stochastic differential equations Stochastic systems Stochastische Differentialgleichung Stochastisches System |
| work_keys_str_mv | AT adomiang stochasticsystems |