Stochastic population processes: analysis, approximations, simulations
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2011
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 628 - 646 |
| Beschreibung: | XII, 652 S. graph. Darst. |
| ISBN: | 9780199575312 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV037318189 | ||
| 003 | DE-604 | ||
| 005 | 20191001 | ||
| 007 | t | ||
| 008 | 110404s2011 xxud||| |||| 00||| eng d | ||
| 010 | |a 2010044096 | ||
| 020 | |a 9780199575312 |9 978-0-19-957531-2 | ||
| 035 | |a (OCoLC)729951737 | ||
| 035 | |a (DE-599)BVBBV037318189 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c US | ||
| 049 | |a DE-20 |a DE-473 |a DE-91G |a DE-11 |a DE-29T |a DE-19 |a DE-83 | ||
| 050 | 0 | |a HB849.4 | |
| 082 | 0 | |a 519.2/33 | |
| 084 | |a MR 2100 |0 (DE-625)123488: |2 rvk | ||
| 084 | |a SK 820 |0 (DE-625)143258: |2 rvk | ||
| 084 | |a WC 7700 |0 (DE-625)148144: |2 rvk | ||
| 084 | |a 92D25 |2 msc | ||
| 084 | |a MAT 607f |2 stub | ||
| 084 | |a 60J20 |2 msc | ||
| 084 | |a BIO 105f |2 stub | ||
| 084 | |a 60J70 |2 msc | ||
| 100 | 1 | |a Renshaw, Eric |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Stochastic population processes |b analysis, approximations, simulations |c Eric Renshaw |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2011 | |
| 300 | |a XII, 652 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz. S. 628 - 646 | ||
| 650 | 4 | |a Population |x Statistical methods | |
| 650 | 4 | |a Markov processes | |
| 650 | 0 | 7 | |a Markov-Prozess |0 (DE-588)4134948-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematische Modellierung |0 (DE-588)7651795-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Bevölkerungsentwicklung |0 (DE-588)4006292-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Markov-Prozess |0 (DE-588)4134948-9 |D s |
| 689 | 0 | 1 | |a Bevölkerungsentwicklung |0 (DE-588)4006292-2 |D s |
| 689 | 0 | 2 | |a Mathematische Modellierung |0 (DE-588)7651795-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022472440&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-022472440 | ||
Datensatz im Suchindex
| _version_ | 1804145596163948544 |
|---|---|
| adam_text | Titel: Stochastic population processes
Autor: Renshaw, Eric
Jahr: 2011
Contents
Preface ix
1 Introduction 1
1.1 Some simple stochastic processes 3
1.2 Single-species population dynamics 7
1.3 Bivariate populations 15
1.4 Spatial-temporal processes 21
2 Simple Markov population processes 31
2.1 Simple Poisson process 31
2.1.1 Time to subsequent events 31
2.1.2 Number of events 34
2.1.3 General moments 37
2.1.4 Simulation 40
2.1.5 Generalizations 43
2.1.6 Do moments uniquely define a distribution? 47
2.2 Pure death process 50
2.2.1 Stochastic model 50
2.2.2 Reverse transition probabilities 53
2.2.3 Bridge probabilities 54
2.3 Pure birth process 55
2.3.1 Stochastic model 56
2.3.2 Laplace transform solution 57
2.3.3 Solution via the p.g.f. 59
2.3.4 Time to a given state 60
2.3.5 Generalized birth process 63
2.4 Simple birth-death process 70
2.4.1 Stochastic model 70
2.4.2 Extinction 74
2.4.3 A simple mixture representation 76
2.4.4 The backward equations 77
2.4.5 Time to a given state 79
2.4.6 Reverse transition probabilities 80
2.4.7 Simulating the simple birth-death process 81
2.4.8 The dominant leader process 85
2.5 Simple immigration-birth-death process 86
2.5.1 Stochastic model (A = 0) 87
2.5.2 Stochastic model (A 0) 88
2.5.3 Equilibrium probabilities 90
2.5.4 Perfect simulation 91
2.6 Simple immigration-emigration process 95
2.6.1 Equilibrium distribution 96
2.6.2 Time-dependent solutions 97
2.7 Batch events 101
2.7.1 Birth-mass annihilation and immigration process 101
2.7.2 Mass immigration-death process 103
2.7.3 Regenerative phenomena 104
General Markov population processes 107
3.1 Classification of states 108
3.2 Equilibrium solutions 117
3.2.1 Logistic population growth 123
3.2.2 Simulated realizations 126
3.2.3 Multiple equilibria 129
3.2.4 Power-law processes 132
3.3 Time-dependent solutions 141
3.3.1 Approximate solutions 141
3.3.2 Probability of ultimate extinction 143
3.3.3 Mean time to ultimate extinction 145
3.4 Moment closure 148
3.4.1 Cumulant equations 149
3.5 Avoiding the Kolmogorov equations 153
3.5.1 Generating cumulant equations directly 153
3.5.2 Local approximations 156
3.5.3 Application to Africanized honey bees 159
3.6 Diffusion approximations 164
3.6.1 Equilibrium probabilities 165
3.6.2 Perturbation methods 168
3.6.3 Additive mass-immigration process 175
3.7 The saddlepoint approximation 181
3.7.1 Basic derivation 183
3.7.2 Examples 185
3.7.3 Relationship with the Method of Steepest Descents 188
3.7.4 The truncated saddlepoint approximation 190
3.7.5 Final comments 197
The random walk 199
4.1 The simple unrestricted random walk 200
4.1.1 Normal approximation 201
4.1.2 Laws of large numbers 202
4.1.3 Using the reflection principle 203
4.1.4 First passage and return probabilities 206
4.1.5 Probability of long leads: the First Arc Sine Law 208
4.1.6 Simulated illustration 212
4.2 Absorbing barriers 214
4.2.1 Probability of absorption at time n 215
4.2.2 One absorbing barrier 221
4.2.3 Number of steps to absorption 223
4.2.4 Further aspects of the unrestricted random walk 225
4.3 Reflecting barriers 228
4.3.1 General equilibrium probability distribution 228
4.3.2 Relation between reflecting and absorbing barriers 232
4.3.3 Time-dependent probability distribution 234
4.4 The correlated random walk 238
4.4.1 Occupation probabilities: direct solution 239
4.4.2 Occupation probabilities: p.g-f- solution 241
4.4.3 Application to share trading 246
Markov chains 252
5.1 Two-state Markov chain 256
5.1.1 Occupation probabilities 257
5.1.2 Matrix solution 1 258
5.1.3 Matrix solution 2 260
5.1.4 The Discrete Telegraph Wave 261
5.1.5 Relation to the continuous-time process 262
5.2 Examples of m-state Markov chains 265
5.2.1 The Ehrenfest model 265
5.2.2 The Perron-Frobenius Theorem 272
5.3 First return and passage probabilities 274
5.3.1 Classification of states 274
5.3.2 Relating first return and passage probabilities 276
5.3.3 Closed sets of states 280
5.3.4 Irreducible chains 281
5.4 Branching processes 282
5.4.1 Population size moments 283
5.4.2 Probability of extinction 286
5.5 A brief note on martingales 290
Markov processes in continuous time and space 295
6.1 The basic Wiener process 296
6.1.1 Diffusion equations for the Wiener process 298
6.1.2 Wiener process with reflecting barriers 300
6.1.3 Wiener process with absorbing barriers 304
6.2 The Fokker-Planck diffusion equation 309
6.2.1 Simulation of the simple immigration-death diffusion process 312
6.2.2 Equilibrium probability solution 317
6.2.3 Boundary conditions 321
6.2.4 Time-dependent probability solutions 322
6.2.5 The associated stochastic differential equation 323
6.3 The Ornstein-Uhlenbeck process 325
6.3.1 The OU process as a time-transformed Wiener process 329
6.3.2 Rapid oscillations of the Wiener and OU processes 329
7 Modelling bivariate processes 331
7.1 Simple immigration-death-switch process 331
7.1.1 Generating moments 334
7.2 Count-dependent growth 337
7.2.1 Stochastic representation 337
7.3 Bivariate saddlepoint approximation 339
7.3.1 Simple illustrations 340
7.3.2 Cumulant truncation 342
7.3.3 A cautionary tale! 346
7.3.4 A spatial example 347
7.4 Counting processes 349
7.4.1 Paired-immigration-death process 350
7.4.2 Single-paired-immigration-death counting process 353
7.4.3 Batch-immigration-death counting process 357
7.4.4 Summary and further developments 364
7.5 Applying MCMC to hidden event times 367
7.5.1 Introducing Markov chain Monte Carlo 367
7.5.2 Fitting the simple immigration-death process to incomplete
observations 369
7.5.3 Extension to the single/paired-immigration-death process 378
7.5.4 A comparison of Metropolis Q- and direct P-matrix strategies 381
8 Two-species interaction processes 389
8.1 Competition processes 389
8.1.1 Deterministic analysis 390
8.1.2 Stability 393
8.1.3 Stochastic behaviour 398
8.1.4 Moment equations 408
8.2 Predator-prey processes 413
8.2.1 The Lotka-Volterra process 414
8.2.2 The Volterra process 419
8.2.3 A model for prey cover 426
8.2.4 Sustained deterministic and stochastic limit cycles 428
8.3 Epidemic processes 434
8.3.1 Simple epidemic 435
8.3.2 General epidemic 445
8.3.3 Recurrent epidemics 454
8.4 Cumulative size processes 464
8.4.1 Deterministic models 465
8.4.2 Stochastic simulation 466
8.4.3 Probability solutions 468
8.4.4 Power-law processes 471
9 Spatial processes 474
9.1 General results 474
9.2 Two-site models 477
9.2.1 Moments 478
9.2.2 Exact probabilities 481
9.2.3 An approximate stochastic solution 484
9.2.4 Slightly connected processes 488
9.2.5 Sequences of integral equations 490
9.2.6 Riccati representations 493
9.3 Stepping-stone processes 496
9.3.1 Birth-death-migration processes on the infinite line 498
9.3.2 Birth-death-migration processes on the finite line 508
9.3.3 Basic simulation algorithms 514
9.3.4 Tau-leaping and other extensions 519
9.4 Velocities of propagation 524
9.4.1 Wave profiles for two-way migration 526
9.4.2 Wave profiles for non-nearest-neighbour migration 533
9.4.3 Travelling waves 541
9.5 Turing s model for morphogenesis 549
9.5.1 Solution of the linearized equations 551
9.5.2 An example of wave formation 553
9.5.3 Stability and the Stochastic Dynamic 559
9.6 Markov chain approach 561
9.6.1 A more refined approximating process 563
9.6.2 Simulating the Markov chain representation 565
9.6.3 Stochastic cellular automata 567
10 Spatial-temporal extensions 575
10.1 Power-law lattice processes 575
10.1.1 First- and second-order moments 576
10.1.2 The spectrum 578
10.1.3 General power-law spectra 584
10.1.4 The inverse problem 585
10.1.5 Simulated realizations 589
10.1.6 An application to sea waves 592
10.2 Space-time marked point processes 596
10.2.1 The general model 598
10.2.2 Choosing growth and interaction functions 599
10.2.3 Parameter selection 603
10.2.4 Simulation algorithm 604
10.2.5 Convergence issues 608
10.2.6 Application to forestry 610
10.2.7 Application to tightly packed particle systems 613
10.2.8 Other stochastic strategies 619
10.2.9 Final comments 624
References 628
Subject Index 647
|
| any_adam_object | 1 |
| author | Renshaw, Eric |
| author_facet | Renshaw, Eric |
| author_role | aut |
| author_sort | Renshaw, Eric |
| author_variant | e r er |
| building | Verbundindex |
| bvnumber | BV037318189 |
| callnumber-first | H - Social Science |
| callnumber-label | HB849 |
| callnumber-raw | HB849.4 |
| callnumber-search | HB849.4 |
| callnumber-sort | HB 3849.4 |
| callnumber-subject | HB - Economic Theory and Demography |
| classification_rvk | MR 2100 SK 820 WC 7700 |
| classification_tum | MAT 607f BIO 105f |
| ctrlnum | (OCoLC)729951737 (DE-599)BVBBV037318189 |
| dewey-full | 519.2/33 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/33 |
| dewey-search | 519.2/33 |
| dewey-sort | 3519.2 233 |
| dewey-tens | 510 - Mathematics |
| discipline | Biologie Soziologie Mathematik |
| edition | 1. publ. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01993nam a2200541 c 4500</leader><controlfield tag="001">BV037318189</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20191001 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">110404s2011 xxud||| |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2010044096</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780199575312</subfield><subfield code="9">978-0-19-957531-2</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)729951737</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV037318189</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-20</subfield><subfield code="a">DE-473</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-83</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">HB849.4</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.2/33</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MR 2100</subfield><subfield code="0">(DE-625)123488:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 820</subfield><subfield code="0">(DE-625)143258:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">WC 7700</subfield><subfield code="0">(DE-625)148144:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">92D25</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 607f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">60J20</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">BIO 105f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">60J70</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Renshaw, Eric</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Stochastic population processes</subfield><subfield code="b">analysis, approximations, simulations</subfield><subfield code="c">Eric Renshaw</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">1. publ.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Oxford [u.a.]</subfield><subfield code="b">Oxford Univ. Press</subfield><subfield code="c">2011</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XII, 652 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturverz. S. 628 - 646</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Population</subfield><subfield code="x">Statistical methods</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Markov processes</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Markov-Prozess</subfield><subfield code="0">(DE-588)4134948-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematische Modellierung</subfield><subfield code="0">(DE-588)7651795-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Bevölkerungsentwicklung</subfield><subfield code="0">(DE-588)4006292-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Markov-Prozess</subfield><subfield code="0">(DE-588)4134948-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Bevölkerungsentwicklung</subfield><subfield code="0">(DE-588)4006292-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Mathematische Modellierung</subfield><subfield code="0">(DE-588)7651795-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022472440&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-022472440</subfield></datafield></record></collection> |
| id | DE-604.BV037318189 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T23:21:58Z |
| institution | BVB |
| isbn | 9780199575312 |
| language | English |
| lccn | 2010044096 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-022472440 |
| oclc_num | 729951737 |
| open_access_boolean | |
| owner | DE-20 DE-473 DE-BY-UBG DE-91G DE-BY-TUM DE-11 DE-29T DE-19 DE-BY-UBM DE-83 |
| owner_facet | DE-20 DE-473 DE-BY-UBG DE-91G DE-BY-TUM DE-11 DE-29T DE-19 DE-BY-UBM DE-83 |
| physical | XII, 652 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| spelling | Renshaw, Eric Verfasser aut Stochastic population processes analysis, approximations, simulations Eric Renshaw 1. publ. Oxford [u.a.] Oxford Univ. Press 2011 XII, 652 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 628 - 646 Population Statistical methods Markov processes Markov-Prozess (DE-588)4134948-9 gnd rswk-swf Mathematische Modellierung (DE-588)7651795-0 gnd rswk-swf Bevölkerungsentwicklung (DE-588)4006292-2 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 s Bevölkerungsentwicklung (DE-588)4006292-2 s Mathematische Modellierung (DE-588)7651795-0 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022472440&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Renshaw, Eric Stochastic population processes analysis, approximations, simulations Population Statistical methods Markov processes Markov-Prozess (DE-588)4134948-9 gnd Mathematische Modellierung (DE-588)7651795-0 gnd Bevölkerungsentwicklung (DE-588)4006292-2 gnd |
| subject_GND | (DE-588)4134948-9 (DE-588)7651795-0 (DE-588)4006292-2 |
| title | Stochastic population processes analysis, approximations, simulations |
| title_auth | Stochastic population processes analysis, approximations, simulations |
| title_exact_search | Stochastic population processes analysis, approximations, simulations |
| title_full | Stochastic population processes analysis, approximations, simulations Eric Renshaw |
| title_fullStr | Stochastic population processes analysis, approximations, simulations Eric Renshaw |
| title_full_unstemmed | Stochastic population processes analysis, approximations, simulations Eric Renshaw |
| title_short | Stochastic population processes |
| title_sort | stochastic population processes analysis approximations simulations |
| title_sub | analysis, approximations, simulations |
| topic | Population Statistical methods Markov processes Markov-Prozess (DE-588)4134948-9 gnd Mathematische Modellierung (DE-588)7651795-0 gnd Bevölkerungsentwicklung (DE-588)4006292-2 gnd |
| topic_facet | Population Statistical methods Markov processes Markov-Prozess Mathematische Modellierung Bevölkerungsentwicklung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022472440&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT renshaweric stochasticpopulationprocessesanalysisapproximationssimulations |