000			04748nam a22004333i 4500
001			EBC5123119
003			MiAaPQ
005			20240729131548.0
006			m o d |
007			cr cnu||||||||
008			240724s2017 xx o ||||0 eng d
020			_a9781119473558 _q(electronic bk.)
020			_z9781786302526
035			_a(MiAaPQ)EBC5123119
035			_a(Au-PeEL)EBL5123119
035			_a(CaPaEBR)ebr11464347
035			_a(OCoLC)1009042545
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA274.76 .K477 2017
100	1		_aKersting, Götz.
245	1	0	_aDiscrete Time Branching Processes in Random Environment.
250			_a1st ed.
264		1	_aNewark : _bJohn Wiley & Sons, Incorporated, _c2017.
264		4	_c©2017.
300			_a1 online resource (311 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
505	0		_aCover -- Half-Title Page -- Title Page -- Copyright Page -- Contents -- Preface -- List of Notations -- 1. Branching Processes in Varying Environment -- 1.1. Introduction -- 1.2. Extinction probabilities -- 1.3. Almost sure convergence -- 1.4. Family trees -- 1.4.1. Construction of the Geiger tree -- 1.4.2. Construction of the size-biased tree T* -- 1.5. Notes -- 2. Branching Processes in Random Environment -- 2.1. Introduction -- 2.2. Extinction probabilities -- 2.3. Exponential growth in the supercritical case -- 2.4. Three subcritical regimes -- 2.5. The strictly critical case -- 2.6. Notes -- 3. Large Deviations for BPREs -- 3.1. Introduction -- 3.2. A tail estimate for branching processes in a varying environment -- 3.3. Proof of Theorem 3.1 -- 3.4. Notes -- 4. Properties of Random Walks -- 4.1. Introduction -- 4.2. Sparre-Andersen identities -- 4.3. Spitzer identity -- 4.4. Applications of Sparre-Andersen and Spitzer identities -- 4.4.1. Properties of ladder epochs and ladder heights -- 4.4.2. Tail distributions of ladder epochs -- 4.4.3. Some renewal functions -- 4.4.4. Asymptotic properties of Ln and Mn -- 4.4.5. Arcsine law -- 4.4.6. Large deviations for random walks -- 4.5. Notes -- 5. Critical BPREs: the Annealed Approach -- 5.1. Introduction -- 5.2. Changes of measures -- 5.3. Properties of the prospective minima -- 5.4. Survival probability -- 5.5. Limit theorems for the critical case (annealed approach) -- 5.6. Environment providing survival -- 5.7. Convergence of log Zn -- 5.8. Notes -- 6. Critical BPREs: the Quenched Approach -- 6.1. Introduction -- 6.2. Changes of measures -- 6.3. Probability of survival -- 6.4. Yaglom limit theorems -- 6.4.1. The population size at non-random moments -- 6.4.2. The population size at moments nt, 0 &lt -- t &lt -- 1 -- 6.4.3. The number of particles at moment τ(n) ≤ nt.
505	8		_a6.4.4. The number of particles at moment τ(n) &gt -- nt -- 6.5. Discrete limit distributions -- 6.6. Notes -- 7. Weakly Subcritical BPREs -- 7.1. Introduction -- 7.2. The probability measures P+ and P− -- 7.3. Proof of theorems -- 7.3.1. Proof of Theorem 7.1 -- 7.3.2. Proof of Theorem 7.2 -- 7.3.3. Proof of Theorem 7.3 -- 7.4. Notes -- 8. Intermediate Subcritical BPREs -- 8.1. Introduction -- 8.2. Proof of Theorems 8.1 to 8.3 -- 8.3. Further limit results -- 8.4. Conditioned family trees -- 8.5. Proof of Theorem 8.4 -- 8.6. Notes -- 9. Strongly Subcritical BPREs -- 9.1. Introduction -- 9.2. Survival probability and Yaglom-type limit theorems -- 9.3. Environments providing survival and dynamics of the population size -- 9.3.1. Properties of the transition matrix P* -- 9.3.2. Proof of Theorem 9.2 -- 9.3.3. Proof of Theorem 9.3 -- 9.4. Notes -- 10. Multi-type BPREs -- 10.1. Introduction -- 10.2. Supercritical MBPREs -- 10.3. The survival probability of subcritical and critical MBPREs -- 10.4. Functional limit theorem in the critical case -- 10.5. Subcritical multi-type case -- Appendix -- A.1. Examples of slowly varying functions -- Bibliography -- Index -- Other titles from iSTE in Mathematics and Statistics -- EULA.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aBranching processes.
655		4	_aElectronic books.
700	1		_aVatutin, Vladimir.
776	0	8	_iPrint version: _aKersting, Götz _tDiscrete Time Branching Processes in Random Environment _dNewark : John Wiley & Sons, Incorporated,c2017 _z9781786302526
797	2		_aProQuest (Firm)
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5123119 _zClick to View
999			_c132242 _d132242