Holdings: Stochastic processes

Stochastic processes:

Saved in:

Bibliographic Details
Main Author:	Ross, Sheldon M. 1943- (Author)
Format:	Book
Language:	English
Published:	New York, NY [u.a.] Wiley 1996
Edition:	2. ed.
Series:	Wiley series in probability and mathematical statistics
Subjects:	Stochastic processes Stochastischer Prozess
Online Access:	Publisher description Table of Contents Inhaltsverzeichnis
Item Description:	Hier auch später erschienene, unveränderte Nachdrucke
Physical Description:	XV, 510 S. graph. Darst.
ISBN:	0471120626

Staff View

MARC


LEADER	00000nam a2200000 c 4500
001	BV010838123
003	DE-604
005	20160817
007	t
008	960709s1996 xxud\|\|\| \|\|\|\| 00\|\|\| eng d
020			\|a 0471120626 \|9 0-471-12062-6
020			\|z 9788126517570 \|9 978-81-265-1757-0
035			\|a (OCoLC)263619005
035			\|a (DE-599)BVBBV010838123
040			\|a DE-604 \|b ger \|e rakwb
041	0		\|a eng
044			\|a xxu \|c XD-US
049			\|a DE-91 \|a DE-945 \|a DE-703 \|a DE-384 \|a DE-29T \|a DE-29 \|a DE-20 \|a DE-521 \|a DE-634 \|a DE-11 \|a DE-523
050		0	\|a QA274.R65 1996
082	0		\|a 519.2 20
084			\|a QH 237 \|0 (DE-625)141552: \|2 rvk
084			\|a SK 820 \|0 (DE-625)143258: \|2 rvk
084			\|a WC 7000 \|0 (DE-625)148142: \|2 rvk
084			\|a MAT 605f \|2 stub
100	1		\|a Ross, Sheldon M. \|d 1943- \|e Verfasser \|0 (DE-588)123762235 \|4 aut
245	1	0	\|a Stochastic processes \|c Sheldon M. Ross
250			\|a 2. ed.
264		1	\|a New York, NY [u.a.] \|b Wiley \|c 1996
300			\|a XV, 510 S. \|b graph. Darst.
336			\|b txt \|2 rdacontent
337			\|b n \|2 rdamedia
338			\|b nc \|2 rdacarrier
490	0		\|a Wiley series in probability and mathematical statistics
500			\|a Hier auch später erschienene, unveränderte Nachdrucke
650		4	\|a Stochastic processes
650	0	7	\|a Stochastischer Prozess \|0 (DE-588)4057630-9 \|2 gnd \|9 rswk-swf
689	0	0	\|a Stochastischer Prozess \|0 (DE-588)4057630-9 \|D s
689	0		\|5 DE-604
856	4		\|u http://www.loc.gov/catdir/description/wiley033/95038012.html \|3 Publisher description
856	4		\|u http://www.loc.gov/catdir/toc/onix04/95038012.html \|3 Table of Contents
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=007244772&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA \|3 Inhaltsverzeichnis
999			\|a oai:aleph.bib-bvb.de:BVB01-007244772

Record in the Search Index

_version_	1804125325602324480
adam_text	Contents CHAPTER 1. PRELIMINARIES 1 1.1. Probability 1 1.2. Random Variables 7 1.3. Expected Value 9 1.4. Moment Generating, Characteristic Functions, and Laplace Transforms 15 1.5. Conditional Expectation 20 1.5.1. Conditional Expectations and Bayes Estimators 33 1.6. The Exponential Distribution, Lack of Memory, and Hazard Rate Functions 35 1.7. Some Probability Inequalities 39 1.8. Limit Theorems 41 1.9. Stochastic Processes 41 Problems 46 References 55 Appendix 56 CHAPTER 2. THE POISSON PROCESS 59 2.1. The Poisson Process 59 2.2. Interarrival and Waiting Time Distributions 64 2.3. Conditional Distribution of the Arrival Times 66 2.3.1. The M/G/l Busy Period 73 2.4. Nonhomogeneous Poisson Process 78 2.5. Compound Poisson Random Variables and Processes 82 2.5.1. A Compound Poisson Identity 84 2.5.2. Compound Poisson Processes 87 id Xii CONTENTS 2.6. Conditional Poisson Processes 88 Problems 89 References 97 CHAPTER 3. RENEWAL THEORY 98 3.1. Introduction and Preliminaries 98 3.2. Distribution of N(t) 99 3.3. Some Limit Theorems 101 3.3.1. Wald s Equation 104 3.3.2. Back to Renewal Theory 106 3.4. The Key Renewal Theorem and Applications 109 3.4.1. Alternating Renewal Processes 114 3.4.2. Limiting Mean Excess and Expansion of m{t) 119 3.4.3. Age Dependent Branching Processes 121 3.5. Delayed Renewal Processes 123 3.6. Renewal Reward Processes 132 3.6.1. A Queueing Application 138 3.7. Regenerative Processes 140 3.7.1. The Symmetric Random Walk and the Arc Sine Laws 142 3.8. Stationary Point Processes 149 Problems 153 References 161 CHAPTER 4. MARKOV CHAINS 163 4.1. Introduction and Examples 163 4.2. Chapman Kolmogorov Equations and Classification of States 167 4.3. Limit Theorems 173 4.4. Transitions among Classes, the Gambler s Ruin Problem, and Mean Times in Transient States 185 4.5. Branching Processes 191 4.6. Applications of Markov Chains 193 4.6.1. A Markov Chain Model of Algorithmic Efficiency 193 4.6.2. An Application to Runs—A Markov Chain with a Continuous State Space 195 4.6.3. List Ordering Rules—Optimality of the Transposition Rule 198 CONTENTS Xili 4.7. Time Reversible Markov Chains 203 4.8. Semi Markov Processes 213 Problems 219 References 230 CHAPTER 5. CONTINUOUS TIME MARKOV CHAINS 231 5.1. Introduction 231 5.2. Continuous Time Markov Chains 231 5.3. Birth and Death Processes 233 5.4. The Kolmogorov Differential Equations 239 5.4.1. Computing the Transition Probabilities 249 5.5. Limiting Probabilities 251 5.6. Time Reversibility 257 5.6.1. Tandem Queues 262 5.6.2. A Stochastic Population Model 263 5.7. Applications of the Reversed Chain to Queueing Theory 270 5.7.1. Network of Queues 271 5.7.2. The Erlang Loss Formula 275 5.7.3. The M/G/l Shared Processor System 278 5.8. Uniformization 282 Problems 286 References 294 CHAPTER 6. MARTINGALES 295 Introduction 295 6.1. Martingales 295 6.2. Stopping Times 298 6.3. Azuma s Inequality for Martingales 305 6.4. Submartingales, Supermartingales, and the Martingale Convergence Theorem 313 6.5. A Generalized Azuma Inequality 319 Problems 322 References 327 CHAPTER 7. RANDOM WALKS 328 Introduction 328 7.1. Duality in Random Walks 329 xiv CONTENTS 7.2. Some Remarks Concerning Exchangeable Random Variables 338 7.3. Using Martingales to Analyze Random Walks 341 7.4. Applications to GIG/1 Queues and Ruin Problems 344 7.4.1. The G/G/l Queue 344 7.4.2. A Ruin Problem 347 7.5. Blackwell s Theorem on the Line 349 Problems 352 References 355 CHAPTER 8. BROWNIAN MOTION AND OTHER MARKOV PROCESSES 356 8.1. Introduction and Preliminaries 356 8.2. Hitting Times, Maximum Variable, and Arc Sine Laws 363 8.3. Variations on Brownian Motion 366 8.3.1. Brownian Motion Absorbed at a Value 366 8.3.2. Brownian Motion Reflected at the Origin 368 8.3.3. Geometric Brownian Motion 368 8.3.4. Integrated Brownian Motion 369 8.4. Brownian Motion with Drift 372 8.4.1. Using Martingales to Analyze Brownian Motion 381 8.5. Backward and Forward Diffusion Equations 383 8.6. Applications of the Kolmogorov Equations to Obtaining Limiting Distributions 385 8.6.1. Semi Markov Processes 385 8.6.2. The Ml Gil Queue 388 8.6.3. A Ruin Problem in Risk Theory 392 8.7. A Markov Shot Noise Process 393 8.8. Stationary Processes 396 Problems 399 References 403 CHAPTER 9. STOCHASTIC ORDER RELATIONS 404 Introduction 404 9.1. Stochastically Larger 404 CONTENTS XV 9.2. Coupling 409 9.2.1. Stochastic Monotonicity Properties of Birth and Death Processes 416 9.2.2. Exponential Convergence in Markov Chains 418 9.3. Hazard Rate Ordering and Applications to Counting Processes 420 9.4. Likelihood Ratio Ordering 428 9.5. Stochastically More Variable 433 9.6. Applications of Variability Orderings 437 9.6.1. Comparison of G/G/l Queues 439 9.6.2. A Renewal Process Application 440 9.6.3. A Branching Process Application 443 9.7. Associated Random Variables 446 Problems 449 References 456 CHAPTER 10. POISSON APPROXIMATIONS 457 Introduction 457 10.1. Brun s Sieve 457 10.2. The Stein Chen Method for Bounding the Error of the Poisson Approximation 462 10.3. Improving the Poisson Approximation 467 Problems 470 References 472 ANSWERS AND SOLUTIONS TO SELECTED PROBLEMS 473 INDEX SOS
any_adam_object	1
author	Ross, Sheldon M. 1943-
author_GND	(DE-588)123762235
author_facet	Ross, Sheldon M. 1943-
author_role	aut
author_sort	Ross, Sheldon M. 1943-
author_variant	s m r sm smr
building	Verbundindex
bvnumber	BV010838123
callnumber-first	Q - Science
callnumber-label	QA274
callnumber-raw	QA274.R65 1996
callnumber-search	QA274.R65 1996
callnumber-sort	QA 3274 R65 41996
callnumber-subject	QA - Mathematics
classification_rvk	QH 237 SK 820 WC 7000
classification_tum	MAT 605f
ctrlnum	(OCoLC)263619005 (DE-599)BVBBV010838123
dewey-full	519.220
dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	519 - Probabilities and applied mathematics
dewey-raw	519.2 20
dewey-search	519.2 20
dewey-sort	3519.2 220
dewey-tens	510 - Mathematics
discipline	Biologie Mathematik Wirtschaftswissenschaften
edition	2. ed.
format	Book
fullrecord	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01888nam a2200469 c 4500</leader><controlfield tag="001">BV010838123</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20160817 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">960709s1996 xxud\|\|\| \|\|\|\| 00\|\|\| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0471120626</subfield><subfield code="9">0-471-12062-6</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9788126517570</subfield><subfield code="9">978-81-265-1757-0</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)263619005</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV010838123</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</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">XD-US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91</subfield><subfield code="a">DE-945</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-29</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-521</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-523</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA274.R65 1996</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.2 20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">QH 237</subfield><subfield code="0">(DE-625)141552:</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 7000</subfield><subfield code="0">(DE-625)148142:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 605f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Ross, Sheldon M.</subfield><subfield code="d">1943-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)123762235</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Stochastic processes</subfield><subfield code="c">Sheldon M. Ross</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2. ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York, NY [u.a.]</subfield><subfield code="b">Wiley</subfield><subfield code="c">1996</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XV, 510 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="490" ind1="0" ind2=" "><subfield code="a">Wiley series in probability and mathematical statistics</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Hier auch später erschienene, unveränderte Nachdrucke</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Stochastic processes</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Stochastischer Prozess</subfield><subfield code="0">(DE-588)4057630-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Stochastischer Prozess</subfield><subfield code="0">(DE-588)4057630-9</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=" "><subfield code="u">http://www.loc.gov/catdir/description/wiley033/95038012.html</subfield><subfield code="3">Publisher description</subfield></datafield><datafield tag="856" ind1="4" ind2=" "><subfield code="u">http://www.loc.gov/catdir/toc/onix04/95038012.html</subfield><subfield code="3">Table of Contents</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=007244772&sequence=000002&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:BVB01-007244772</subfield></datafield></record></collection>
id	DE-604.BV010838123
illustrated	Illustrated
indexdate	2024-07-09T17:59:46Z
institution	BVB
isbn	0471120626
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-007244772
oclc_num	263619005
open_access_boolean
owner	DE-91 DE-BY-TUM DE-945 DE-703 DE-384 DE-29T DE-29 DE-20 DE-521 DE-634 DE-11 DE-523
owner_facet	DE-91 DE-BY-TUM DE-945 DE-703 DE-384 DE-29T DE-29 DE-20 DE-521 DE-634 DE-11 DE-523
physical	XV, 510 S. graph. Darst.
publishDate	1996
publishDateSearch	1996
publishDateSort	1996
publisher	Wiley
record_format	marc
series2	Wiley series in probability and mathematical statistics
spelling	Ross, Sheldon M. 1943- Verfasser (DE-588)123762235 aut Stochastic processes Sheldon M. Ross 2. ed. New York, NY [u.a.] Wiley 1996 XV, 510 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and mathematical statistics Hier auch später erschienene, unveränderte Nachdrucke Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s DE-604 http://www.loc.gov/catdir/description/wiley033/95038012.html Publisher description http://www.loc.gov/catdir/toc/onix04/95038012.html Table of Contents HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007244772&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Ross, Sheldon M. 1943- Stochastic processes Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd
subject_GND	(DE-588)4057630-9
title	Stochastic processes
title_auth	Stochastic processes
title_exact_search	Stochastic processes
title_full	Stochastic processes Sheldon M. Ross
title_fullStr	Stochastic processes Sheldon M. Ross
title_full_unstemmed	Stochastic processes Sheldon M. Ross
title_short	Stochastic processes
title_sort	stochastic processes
topic	Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd
topic_facet	Stochastic processes Stochastischer Prozess
url	http://www.loc.gov/catdir/description/wiley033/95038012.html http://www.loc.gov/catdir/toc/onix04/95038012.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007244772&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT rosssheldonm stochasticprocesses

Holdings

There is no print copy available.

Interlibrary loan Place Request Caution: Not in THWS collection! Indexes

MARC

Record in the Search Index

There is no print copy available.

Similar Items