Piecewise deterministic processes in biological models:
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| Format: | Electronic eBook |
| Language: | English |
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[2017]
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| Series: | SpringerBriefs in applied sciences and technology. Mathematical methods
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| Online Access: | BTU01 FHR01 FRO01 FWS01 FWS02 HTW01 TUM01 UBM01 UBT01 UBW01 UEI01 UPA01 Volltext Inhaltsverzeichnis |
| Physical Description: | 1 Online-Ressource (IX, 169 Seiten, 10 illus) |
| ISBN: | 9783319612959 |
| ISSN: | 2191-530X |
| DOI: | 10.1007/978-3-319-61295-9 |
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| adam_text | Preface
e National Science Centre (Poland)
arc grateful to Michael C Mackey
‘pt and made useful suggestions for
Ryszard Rudnicki
Marta Tyran-Kaminska
ontents
Biological Models
1 1 Introduction
1 2 Birth-Death Processes
1 3 Grasshopper and Kangaroo Movement
1 4 Velocity Jump Process
1 5 Size of Cells in a Single Line
1 6 Two-Phase Cell Cycle Model
1 7 Stochastic Billiard as a Cell Cycle Model
1 8 Stochastic Gene Expression I
1 9 Stochastic Gene Expression II
1 10 Gene Regulatory Models with Bursting
1 11 Neural Activity
1 12 Processes with Extra Jumps on a Subspace
1 13 Size-Structured Population Model
1 14 Age-Structured Population Model
1 15 Asexual Phenotype Population Model
1 16 Phenotype Model with a Sexual Reproduction
1 17 Coagulation-Fragmentation Process in a Phytoplankton
Model
1 18 Paralog Families
1 19 Definition of PDMP
Markov Processes
2 1 Transition Probabilities and Kernels
211 Basic Concepts
212 Transition Operators
213 Substochastic and Stochastic Operators
214 Integral Stochastic Operators
215 Frobenius-Perron Operator
216 Iterated Function Systems
1
1
2
3
4
5
7
9
11
13
16
17
19
21
24
25
26
28
29
30
33
33
33
36
38
39
41
42
Vll
viii Contents
2 2 Discrete-Time Markov Processes 44
221 Markov Processes and Transition Probabilities 44
222 Random Mapping Representations 46
223 Canonical Processes 47
2 3 Continuous-Time Markov Processes 49
231 Basic Definitions 49
232 Processes with Stationary and Independent
Increments 51
233 Markov Jump-Type Processes 52
234 Generators and Martingales 54
235 Existence of PDMPs 56
236 Transition Functions and Generators of PDMPs 59
3 Operator Semigroups 63
3 1 Generators and Semigroups 63
311 Essentials of Banach Spaces and Operators 63
312 Definitions and Basic Properties 65
313 The Resolvent 67
3 2 Basic Examples of Semigroups 69
321 Uniformly Continuous Semigroups 69
322 Multiplication Semigroups 70
323 Translation Semigroups 71
3 3 Generators of Contraction Semigroups 73
331 The Hille-Yosida Theorem 73
332 The Lumer-Phillips Theorem 76
333 Perturbations of Semigroups 78
334 Perturbing Boundary Conditions 80
■■■s
4 Stochastic Semigroups 83
4 1 Aspects of Positivity 83
411 Positive Operators 83
412 Substochastic Semigroups 84 ;
413 Resolvent Positive Operators 86
414 Generation Theorems 87 :
415 Positive Perturbations 88
416 Positive Unbounded Perturbations 91
417 Adjoint and Transition Semigroups 94
4 2 Stochastic Semigroups for PDMPs 96
421 Jump-Type Markov Processes 96
422 Semigroups for Semiflows 99
423 PDMPs Without Boundaries 101
424 Dynamical Systems with Jumps 103
425 Randomly Switched Dynamical Systems 104
Contents
4 2 6
4 2 7
Jumps from Boun
Semigroups for
5 1
5 1 2
5 1 3
Asymptotic Properties of S
Results
Asymptotic Stability and
511 Definitions of As
Lower Function
Partially Integral
Stability
Sweeping via the
Function
Asymptotic Decompositi
521 Theorem on As
522 Sweeping and th
523 Asymptotic Stab’
524 Hasminskil Func
5 1 4
5 2
Asymptotic Properties of S
6 1 2
6 1 3
6 1 4
6 1 5
6 2
6 3
Continuous-Time Mark
611 Foguel Altemad
Non-explosive
Stability
Markov Chain
Asymptotics of
Applications to
Dynamical Systems wi
621 General Formal
622 Applications to
Cell Maturation Model
631 Introductory Re
Flows with J
Size-Structured
Two-Phase Cell
Lebowitz-Rub’
Stein’s Model
6 3 2
6 3 3
6 3 4
6 3 5
6 3 6
pendix A: Measure and
erences
ex
Contents
ix
ransition Probabilities
sentations
ses
and Independent
44
44
46
47
49
49
51
sses 52
es 54
56
Generators of PDMPs 59
63
63
and Operators 63
es 65
67
69
’groups 69
70
71
ups 73
73
m 76
s 78
tions 80
83
83
83
84
86
87
88
tions 91
ups 94
96
96
99
101
s 103
Systems 104
J426 Jumps from Boundaries
■% 427 Semigroups for the Stein Model
$■
Asymptotic Properties of Stochastic Semigroups—General
ff Results
5 1 Asymptotic Stability and Sweeping
;511 Definitions of Asymptotic Stability and Sweeping
I512 Lower Function Theorem
|513 Partially Integral Semigroups and Asymptotic
| Stability
|514 Sweeping via the Existence of c-finite Invariant
| Function
5 2 Asymptotic Decomposition of Stochastic Semigroups
521 Theorem on Asymptotic Decomposition
522 Sweeping and the Foguel Alternative
523 Asymptotic Stability
524 Hasminskii Function
6 Asymptotic Properties of Stochastic Semigroups—Applications
6 1 Continuous-Time Markov Chains
611 Foguel Alternative
612 Non-explosive Markov Chains and Asymptotic
Stability
613 Markov Chain with an Absorbing State
614 Asymptotics of Paralog Families
615 Applications to Pure Jump-Type Markov Processes
6 2 Dynamical Systems with Random Switching
621 General Formulation
622 Applications to Stochastic Gene Expression Models
6 3 Cell Maturation Models
631 Introductory Remarks
632 Flows with Jumps
633 Size-Structured Model
634 Two-Phase Cell Cycle Model
635 Lebowitz-Rubinow’s Model
636 Stein’s Model
Appendix A: Measure and Probability Essentials
References
Index
106
109
115
115
115
116
117
118
120
120
122
124
125
129
129
129
130
131
132
133
135
135
137
140
140
141
142
144
146
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159
|
| any_adam_object | 1 |
| author | Rudnicki, Ryszard Tyran-Kamińska, Marta |
| author_GND | (DE-588)173814263 |
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| author_role | aut aut |
| author_sort | Rudnicki, Ryszard |
| author_variant | r r rr m t k mtk |
| building | Verbundindex |
| bvnumber | BV044432824 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA |
| ctrlnum | (ZDB-2-SMA)9783319612959 (OCoLC)1002252598 (DE-599)BVBBV044432824 |
| dewey-full | 576.58 577.88 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 576 - Genetics and evolution 577 - Ecology |
| dewey-raw | 576.58 577.88 |
| dewey-search | 576.58 577.88 |
| dewey-sort | 3576.58 |
| dewey-tens | 570 - Biology |
| discipline | Biologie Mathematik |
| doi_str_mv | 10.1007/978-3-319-61295-9 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2025-02-20T06:54:32Z |
| institution | BVB |
| isbn | 9783319612959 |
| issn | 2191-530X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029834182 |
| oclc_num | 1002252598 |
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| publisher | Springer |
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| series2 | SpringerBriefs in applied sciences and technology. Mathematical methods |
| spellingShingle | Rudnicki, Ryszard Tyran-Kamińska, Marta Piecewise deterministic processes in biological models Mathematics Systems biology System theory Probabilities Biomathematics Biomedical engineering Genetics and Population Dynamics Systems Biology Complex Systems Probability Theory and Stochastic Processes Biomedical Engineering Statistical Physics and Dynamical Systems Mathematik |
| title | Piecewise deterministic processes in biological models |
| title_auth | Piecewise deterministic processes in biological models |
| title_exact_search | Piecewise deterministic processes in biological models |
| title_full | Piecewise deterministic processes in biological models Ryszard Rudnicki, Marta Tyran-Kamińska |
| title_fullStr | Piecewise deterministic processes in biological models Ryszard Rudnicki, Marta Tyran-Kamińska |
| title_full_unstemmed | Piecewise deterministic processes in biological models Ryszard Rudnicki, Marta Tyran-Kamińska |
| title_short | Piecewise deterministic processes in biological models |
| title_sort | piecewise deterministic processes in biological models |
| topic | Mathematics Systems biology System theory Probabilities Biomathematics Biomedical engineering Genetics and Population Dynamics Systems Biology Complex Systems Probability Theory and Stochastic Processes Biomedical Engineering Statistical Physics and Dynamical Systems Mathematik |
| topic_facet | Mathematics Systems biology System theory Probabilities Biomathematics Biomedical engineering Genetics and Population Dynamics Systems Biology Complex Systems Probability Theory and Stochastic Processes Biomedical Engineering Statistical Physics and Dynamical Systems Mathematik |
| url | https://doi.org/10.1007/978-3-319-61295-9 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029834182&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT rudnickiryszard piecewisedeterministicprocessesinbiologicalmodels AT tyrankaminskamarta piecewisedeterministicprocessesinbiologicalmodels |