Stochastic Population Theories:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1974
|
| Schriftenreihe: | Lecture Notes in Biomathematics
3 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | These notes serve as an introduction to stochastic theories which are useful in population biology; they are based on a course given at the Courant Institute, New York, in the Spring of 1974. In order to make the material. accessible to a wide audience, it is assumed that the reader has only a slight acquaintance with probability theory and differential equations. The more sophisticated topics, such as the qualitative behavior of nonlinear models, are approached through a succession of simpler problems. Emphasis is placed upon intuitive interpretations, rather than upon formal proofs. In most cases, the reader is referred elsewhere for a rigorous development. On the other hand, an attempt has been made to treat simple, useful models in some detail. Thus these notes complement the existing mathematical literature, and there appears to be little duplication of existing works. The authors are indebted to Miss Jeanette Figueroa for her beautiful and speedy typing of this work. The research was supported by the National Science Foundation under Grant No. GP-32996X3. CONTENTS I. LINEAR MODELS •••••. •••••••••••••••. . ••••••••••••••••••••••••••••••••••••••• 1 1. The Poisson Process ••••••••••••••••••••••••••. ••. •••••••••••. •••••••••• 1 2. Birth and Death Processes 5 2. 1 Linear Birth Process 5 2. 2 Linear Birth and Death Process •••••. ••••••. ••••••••••••••. •••••••• 7 2. 3 Birth and Death with Carrying Capacity ••••••••. •••. ••••••. ••••••. • 16 3. Branching Processes •••••••••••••••••••. •••••••. ••••••••. ••••••••••••••• 20 3. 1 Continuous Time . •••. ••••••••••. •••••••••••••••••••. ••••••••. •••• |
| Beschreibung: | 1 Online-Ressource (VI, 114 p) |
| ISBN: | 9783642808838 9783540070108 |
| ISSN: | 0341-633X |
| DOI: | 10.1007/978-3-642-80883-8 |
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| 500 | |a These notes serve as an introduction to stochastic theories which are useful in population biology; they are based on a course given at the Courant Institute, New York, in the Spring of 1974. In order to make the material. accessible to a wide audience, it is assumed that the reader has only a slight acquaintance with probability theory and differential equations. The more sophisticated topics, such as the qualitative behavior of nonlinear models, are approached through a succession of simpler problems. Emphasis is placed upon intuitive interpretations, rather than upon formal proofs. In most cases, the reader is referred elsewhere for a rigorous development. On the other hand, an attempt has been made to treat simple, useful models in some detail. Thus these notes complement the existing mathematical literature, and there appears to be little duplication of existing works. The authors are indebted to Miss Jeanette Figueroa for her beautiful and speedy typing of this work. | ||
| 500 | |a The research was supported by the National Science Foundation under Grant No. GP-32996X3. CONTENTS I. LINEAR MODELS •••••. •••••••••••••••. . ••••••••••••••••••••••••••••••••••••••• 1 1. The Poisson Process ••••••••••••••••••••••••••. ••. •••••••••••. •••••••••• 1 2. Birth and Death Processes 5 2. 1 Linear Birth Process 5 2. 2 Linear Birth and Death Process •••••. ••••••. ••••••••••••••. •••••••• 7 2. 3 Birth and Death with Carrying Capacity ••••••••. •••. ••••••. ••••••. • 16 3. Branching Processes •••••••••••••••••••. •••••••. ••••••••. ••••••••••••••• 20 3. | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Ludwig, Donald |
| author_facet | Ludwig, Donald |
| author_role | aut |
| author_sort | Ludwig, Donald |
| author_variant | d l dl |
| building | Verbundindex |
| bvnumber | BV042423024 |
| classification_tum | MAT 000 |
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| ctrlnum | (OCoLC)863820833 (DE-599)BVBBV042423024 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-80883-8 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
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| isbn | 9783642808838 9783540070108 |
| issn | 0341-633X |
| language | English |
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| spelling | Ludwig, Donald Verfasser aut Stochastic Population Theories by Donald Ludwig Berlin, Heidelberg Springer Berlin Heidelberg 1974 1 Online-Ressource (VI, 114 p) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Biomathematics 3 0341-633X These notes serve as an introduction to stochastic theories which are useful in population biology; they are based on a course given at the Courant Institute, New York, in the Spring of 1974. In order to make the material. accessible to a wide audience, it is assumed that the reader has only a slight acquaintance with probability theory and differential equations. The more sophisticated topics, such as the qualitative behavior of nonlinear models, are approached through a succession of simpler problems. Emphasis is placed upon intuitive interpretations, rather than upon formal proofs. In most cases, the reader is referred elsewhere for a rigorous development. On the other hand, an attempt has been made to treat simple, useful models in some detail. Thus these notes complement the existing mathematical literature, and there appears to be little duplication of existing works. The authors are indebted to Miss Jeanette Figueroa for her beautiful and speedy typing of this work. The research was supported by the National Science Foundation under Grant No. GP-32996X3. CONTENTS I. LINEAR MODELS •••••. •••••••••••••••. . ••••••••••••••••••••••••••••••••••••••• 1 1. The Poisson Process ••••••••••••••••••••••••••. ••. •••••••••••. •••••••••• 1 2. Birth and Death Processes 5 2. 1 Linear Birth Process 5 2. 2 Linear Birth and Death Process •••••. ••••••. ••••••••••••••. •••••••• 7 2. 3 Birth and Death with Carrying Capacity ••••••••. •••. ••••••. ••••••. • 16 3. Branching Processes •••••••••••••••••••. •••••••. ••••••••. ••••••••••••••• 20 3. 1 Continuous Time . •••. ••••••••••. •••••••••••••••••••. ••••••••. •••• Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Demographie (DE-588)4011412-0 gnd rswk-swf Stochastik (DE-588)4121729-9 gnd rswk-swf Populationsbiologie (DE-588)4046800-8 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Bevölkerungsstruktur (DE-588)4246600-3 gnd rswk-swf Demographie (DE-588)4011412-0 s Stochastik (DE-588)4121729-9 s 1\p DE-604 Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s 2\p DE-604 Populationsbiologie (DE-588)4046800-8 s 3\p DE-604 Bevölkerungsstruktur (DE-588)4246600-3 s 4\p DE-604 https://doi.org/10.1007/978-3-642-80883-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ludwig, Donald Stochastic Population Theories Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Demographie (DE-588)4011412-0 gnd Stochastik (DE-588)4121729-9 gnd Populationsbiologie (DE-588)4046800-8 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Bevölkerungsstruktur (DE-588)4246600-3 gnd |
| subject_GND | (DE-588)4011412-0 (DE-588)4121729-9 (DE-588)4046800-8 (DE-588)4064324-4 (DE-588)4246600-3 |
| title | Stochastic Population Theories |
| title_auth | Stochastic Population Theories |
| title_exact_search | Stochastic Population Theories |
| title_full | Stochastic Population Theories by Donald Ludwig |
| title_fullStr | Stochastic Population Theories by Donald Ludwig |
| title_full_unstemmed | Stochastic Population Theories by Donald Ludwig |
| title_short | Stochastic Population Theories |
| title_sort | stochastic population theories |
| topic | Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Demographie (DE-588)4011412-0 gnd Stochastik (DE-588)4121729-9 gnd Populationsbiologie (DE-588)4046800-8 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Bevölkerungsstruktur (DE-588)4246600-3 gnd |
| topic_facet | Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Demographie Stochastik Populationsbiologie Wahrscheinlichkeitsrechnung Bevölkerungsstruktur |
| url | https://doi.org/10.1007/978-3-642-80883-8 |
| work_keys_str_mv | AT ludwigdonald stochasticpopulationtheories |