This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and…mehr
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
1.- 9. Asymptotic results when m < 1.- 10. Asymptotic results when m = 1.- 11. Stationarity of Zn.- 12. An application of stationary measures.- 13. Further results on the Galton-Watson process and related topics.- II. Processes with a finite number of types.- 1. Introduction.- 2. Definition of the multitype Galton-Watson process.- 3. The basic result for generating functions.- 4. First and second moments; basic assumption.- 5. Positivity properties.- 6. Transience of the nonzero states.- 7. Extinction probability.- 8. A numerical example.- 9. Asymptotic results for large n.- 10. Processes that are not positively regular.- 11. An example from genetics.- 12. Remarks.- III. The general branching process.- 1. Introduction.- 2. Point-distributions and set functions.- 3. Probabilities for point-distributions.- 4. Random integrals.- 5. Moment-generating functionals.- 6. Definition of the general branching process.- 7. Recurrence relation for the moment-generating functionals.- 8. Examples.- 9. First moments.- 10. Existence of eigenfunctions for M.- 11. Transience of Zn.- 12. The case ? ? 1.- 13. Second moments.- 14. Convergence of Zn/?n when ? > 1.- 15. Determination of the extinction probability when ? > l.- 16. Another kind of limit theorem.- 17. Processes with a continuous time parameter.- Appendix 1.- Appendix 2.- Appendix 3.- IV. Neutron branching processes (one-group theory, isotropic case).- 1. Introduction.- 2. Physical description.- 3. Mathematical formulation of the process.- 4. The first moment.-5. Criticality.- 6. Fluctuations; probability of extinction; total number in the critical case.- 7. Continuous time parameter.- 8. Other methods.- 9. Invariance principles.- 10. One-dimensional neutron multiplication.- V. Markov branching processes (continuous time).- 1. Introduction.- 2. Markov branching processes.- 3. Equations for the probabilities.- 4. Generating functions.- 5. Iterative property of F1; the imbedded Galton-Watson process.- 6. Moments.- 7. Example: the birth-and-death process.- 8. YULE'S problem.- 9. The temporally homogeneous case.- 10. Extinction probability.- 11. Asymptotic results.- 12. Stationary measures.- 13. Examples.- 14. Individual probabilities.- 15. Processes with several types.- 16. Additional topics.- Appendix 1.- Appendix 2.- VI. Age-dependent branching processes.- 1. Introduction.- 2. Family histories.- 3. The number of objects at a given time.- 4. The probability measure P.- 5. Sizes of the generations.- 6. Expression of Z (t, ?) as a sum of objects in subfamilies.- 7. Integral equation for the generating function.- 8. The point of regeneration.- 9. Construction and properties of F (s, t).- 10. Joint distribution of Z (t1), Z(t2),. . ., Z (tk).- 11. Markovian character of Z in the exponential case.- 12. A property of the random functions; nonincreasing character of F(1, t).- 13. Conditions for the sequel; finiteness of Z (t) and ? Z (t).- 14. Properties of the sample functions.- 15. Integral equation for M (t) = ? Z (t); monotone character of M.- 16. Calculation of M.- 17. Asymptotic behavior of M; the Malthusian parameter.- 18. Second moments.- 19. Mean convergence of Z (t)/n1 e?t.- 20. Functional equation for the moment-generating function of W.- 21. Probability 1 convergence of Z (t)/n1e?t.- 22. The distribution of W.-23 · Application to colonies of bacteria.- 24. The age distribution.- 25· Convergence of the actual age distribution.- 26. Applications of the age distribution.- 27. Age-dependent branching processes in the extended sense.- 28. Generalizations of the mathematical model.- 29. Age-dependent birth-and-death processes.- VII. Branching processes in the theory of cosmic rays (electronphoton cascades).- 1. Introduction.- 2. Assumptions concerning the electron-photon cascade.- 3. Mathematical assumptions about the functions q and k.- 4. The energy of a single electron (Approximation A).- 5. Explicit representation of ? (t) in terms of jumps.- 6. Distribution of X (t) = - log ? (t) when t is small.- 7. Definition of the electron-photon cascade and of the random variable N(E, t) (Approximation A).- 8. Conservation of energy (Approximation A).- 9. Functional equations.- 10. Some properties of the generating functions and first moments.- 11. Derivation of functional equations for f1 and f2.- 12. Moments of N (E, t).- 13. The expectation process.- 14. Distribution of Z (t) when t is large.- 15. Total energy in the electrons.- 16. Limiting distributions.- 17. The energy of an electron when ß>0 (Approximation B).- 18. The electron-photon cascade (Approximation B).- Appendix 1.- Appendix 2.
1.- 9. Asymptotic results when m < 1.- 10. Asymptotic results when m = 1.- 11. Stationarity of Zn.- 12. An application of stationary measures.- 13. Further results on the Galton-Watson process and related topics.- II. Processes with a finite number of types.- 1. Introduction.- 2. Definition of the multitype Galton-Watson process.- 3. The basic result for generating functions.- 4. First and second moments; basic assumption.- 5. Positivity properties.- 6. Transience of the nonzero states.- 7. Extinction probability.- 8. A numerical example.- 9. Asymptotic results for large n.- 10. Processes that are not positively regular.- 11. An example from genetics.- 12. Remarks.- III. The general branching process.- 1. Introduction.- 2. Point-distributions and set functions.- 3. Probabilities for point-distributions.- 4. Random integrals.- 5. Moment-generating functionals.- 6. Definition of the general branching process.- 7. Recurrence relation for the moment-generating functionals.- 8. Examples.- 9. First moments.- 10. Existence of eigenfunctions for M.- 11. Transience of Zn.- 12. The case ? ? 1.- 13. Second moments.- 14. Convergence of Zn/?n when ? > 1.- 15. Determination of the extinction probability when ? > l.- 16. Another kind of limit theorem.- 17. Processes with a continuous time parameter.- Appendix 1.- Appendix 2.- Appendix 3.- IV. Neutron branching processes (one-group theory, isotropic case).- 1. Introduction.- 2. Physical description.- 3. Mathematical formulation of the process.- 4. The first moment.-5. Criticality.- 6. Fluctuations; probability of extinction; total number in the critical case.- 7. Continuous time parameter.- 8. Other methods.- 9. Invariance principles.- 10. One-dimensional neutron multiplication.- V. Markov branching processes (continuous time).- 1. Introduction.- 2. Markov branching processes.- 3. Equations for the probabilities.- 4. Generating functions.- 5. Iterative property of F1; the imbedded Galton-Watson process.- 6. Moments.- 7. Example: the birth-and-death process.- 8. YULE'S problem.- 9. The temporally homogeneous case.- 10. Extinction probability.- 11. Asymptotic results.- 12. Stationary measures.- 13. Examples.- 14. Individual probabilities.- 15. Processes with several types.- 16. Additional topics.- Appendix 1.- Appendix 2.- VI. Age-dependent branching processes.- 1. Introduction.- 2. Family histories.- 3. The number of objects at a given time.- 4. The probability measure P.- 5. Sizes of the generations.- 6. Expression of Z (t, ?) as a sum of objects in subfamilies.- 7. Integral equation for the generating function.- 8. The point of regeneration.- 9. Construction and properties of F (s, t).- 10. Joint distribution of Z (t1), Z(t2),. . ., Z (tk).- 11. Markovian character of Z in the exponential case.- 12. A property of the random functions; nonincreasing character of F(1, t).- 13. Conditions for the sequel; finiteness of Z (t) and ? Z (t).- 14. Properties of the sample functions.- 15. Integral equation for M (t) = ? Z (t); monotone character of M.- 16. Calculation of M.- 17. Asymptotic behavior of M; the Malthusian parameter.- 18. Second moments.- 19. Mean convergence of Z (t)/n1 e?t.- 20. Functional equation for the moment-generating function of W.- 21. Probability 1 convergence of Z (t)/n1e?t.- 22. The distribution of W.-23 · Application to colonies of bacteria.- 24. The age distribution.- 25· Convergence of the actual age distribution.- 26. Applications of the age distribution.- 27. Age-dependent branching processes in the extended sense.- 28. Generalizations of the mathematical model.- 29. Age-dependent birth-and-death processes.- VII. Branching processes in the theory of cosmic rays (electronphoton cascades).- 1. Introduction.- 2. Assumptions concerning the electron-photon cascade.- 3. Mathematical assumptions about the functions q and k.- 4. The energy of a single electron (Approximation A).- 5. Explicit representation of ? (t) in terms of jumps.- 6. Distribution of X (t) = - log ? (t) when t is small.- 7. Definition of the electron-photon cascade and of the random variable N(E, t) (Approximation A).- 8. Conservation of energy (Approximation A).- 9. Functional equations.- 10. Some properties of the generating functions and first moments.- 11. Derivation of functional equations for f1 and f2.- 12. Moments of N (E, t).- 13. The expectation process.- 14. Distribution of Z (t) when t is large.- 15. Total energy in the electrons.- 16. Limiting distributions.- 17. The energy of an electron when ß>0 (Approximation B).- 18. The electron-photon cascade (Approximation B).- Appendix 1.- Appendix 2.
Es gelten unsere Allgemeinen Geschäftsbedingungen: www.buecher.de/agb
Impressum
www.buecher.de ist ein Internetauftritt der buecher.de internetstores GmbH
Geschäftsführung: Monica Sawhney | Roland Kölbl | Günter Hilger
Sitz der Gesellschaft: Batheyer Straße 115 - 117, 58099 Hagen
Postanschrift: Bürgermeister-Wegele-Str. 12, 86167 Augsburg
Amtsgericht Hagen HRB 13257
Steuernummer: 321/5800/1497
USt-IdNr: DE450055826
