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001 978-1-4614-3688-1
003 DE-He213
005 20140220083248.0
007 cr nn 008mamaa
008 120804s2012 xxu| s |||| 0|eng d
020 _a9781461436881
_9978-1-4614-3688-1
024 7 _a10.1007/978-1-4614-3688-1
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
082 0 4 _a519.2
_223
100 1 _aShiryaev, Albert N.
_eauthor.
245 1 0 _aProblems in Probability
_h[electronic resource] /
_cby Albert N. Shiryaev.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2012.
300 _aXII, 427 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aProblem Books in Mathematics,
_x0941-3502
505 0 _aPreface -- 1. Elementary Probability Theory -- 2. Mathematical Foundations of Probability Theory -- 3. Convergence of Probability Measures -- 4. Independent Random Variables -- 5. Stationary Random Sequences in Strict Sense -- 6. Stationary Random Sequences in Broad Sense -- 7. Martingales -- 8. Markov Chains -- Appendix -- References.
520 _aProblems in Probability  comprises one of the most comprehensive, nearly encyclopedic, collections of problems and exercises in probability theory. Albert Shiryaev has skillfully created, collected, and compiled  the exercises in this text over the course of many years while working on topics which interested him the most.   A substantial  number of the exercises resulted from diverse sources such as textbooks, lecture notes, exercise manuals, monographs, and discussions that took place during special seminars for graduate and undergraduate students. Many problems contain helpful hints and other relevant comments and a portion of the material covers some important applications from optimal control and mathematical finance. Readers of diverse backgrounds—from students to researchers—will find a great deal of value in this book and can treat the work as an exercise manual, a handbook, or as a supplementary text to a course in probability theory, control, and mathematical finance. The problems and exercises in this book vary in nature and degree of difficulty. Some problems are meant to test the reader’s basic understanding, others are of medium-to-high degrees of difficulty and require more creative thinking. Other problems are meant to develop additional theoretical concepts and tools or to familiarize the reader with various facts that are not necessarily covered in mainstream texts. Additional problems are related to the passage from random walk to Brownian motions and Brownian bridges. The appendix contains a summary of the main results, notation and terminology that are used throughout the book.  It also contains additional material from combinatorics, potential theory and Markov chains—subjects that are not covered in the book, but are nevertheless needed for many of the exercises included here.
650 0 _aMathematics.
650 0 _aCombinatorics.
650 0 _aDistribution (Probability theory).
650 1 4 _aMathematics.
650 2 4 _aProbability Theory and Stochastic Processes.
650 2 4 _aCombinatorics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461436874
830 0 _aProblem Books in Mathematics,
_x0941-3502
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-3688-1
912 _aZDB-2-SMA
999 _c101425
_d101425