000			04302nam a22004935i 4500
001			978-3-642-37632-0
003			DE-He213
005			20140220082517.0
007			cr nn 008mamaa
008			140109s2014 gw | s |||| 0|eng d
020			_a9783642376320 _9978-3-642-37632-0
024	7		_a10.1007/978-3-642-37632-0 _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		_aKyprianou, Andreas E. _eauthor.
245	1	0	_aFluctuations of Lévy Processes with Applications _h[electronic resource] : _bIntroductory Lectures / _cby Andreas E. Kyprianou.
250			_a2nd ed. 2014.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c2014.
300			_aXVIII, 455 p. 26 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aUniversitext, _x0172-5939
505	0		_a1.Lévy Processes and Applications -- 2.The Lévy–Itô Decomposition and Path Structure -- 3.More Distributional and Path-Related Properties -- 4.General Storage Models and Paths of Bounded Variation -- 5.Subordinators at First Passage and Renewal Measures -- 6.The Wiener–Hopf Factorisation -- 7.Lévy Processes at First Passage -- 8.Exit Problems for Spectrally Negative Processes -- 9.More on Scale Functions -- 10.Ruin Problems and Gerber-Shiu Theory -- 11.Applications to Optimal Stopping Problems -- 12.Continuous-State Branching Processes -- 13.Positive Self-similar Markov Processes -- Epilogue -- Hints for Exercises -- References -- Index.
520			_aLévy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their application appears in the theory of many areas of classical and modern stochastic processes including storage models, renewal processes, insurance risk models, optimal stopping problems, mathematical finance, continuous-state branching processes and positive self-similar Markov processes. This textbook is based on a series of graduate courses concerning the theory and application of Lévy processes from the perspective of their path fluctuations. Central to the presentation is the decomposition of paths in terms of excursions from the running maximum as well as an understanding of short- and long-term behaviour. The book aims to be mathematically rigorous while still providing an intuitive feel for underlying principles. The results and applications often focus on the case of Lévy processes with jumps in only one direction, for which recent theoretical advances have yielded a higher degree of mathematical tractability. The second edition additionally addresses recent developments in the potential analysis of subordinators, Wiener-Hopf theory, the theory of scale functions and their application to ruin theory, as well as including an extensive overview of the classical and modern theory of positive self-similar Markov processes. Each chapter has a comprehensive set of exercises. Andreas Kyprianou has a degree in Mathematics from the University of Oxford and a Ph.D. in Probability Theory from The University of Sheffield. He is currently a Professor of Probability at the University of Bath, having held academic positions in Mathematics and Statistics Departments at the London School of Economics, Edinburgh University, Utrecht University and Heriot-Watt University, besides working for nearly two years as a research mathematician in the oil industry. His research is focused on pure and applied probability.
650		0	_aMathematics.
650		0	_aFinance.
650		0	_aDistribution (Probability theory).
650	1	4	_aMathematics.
650	2	4	_aProbability Theory and Stochastic Processes.
650	2	4	_aQuantitative Finance.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783642376313
830		0	_aUniversitext, _x0172-5939
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-642-37632-0
912			_aZDB-2-SMA
999			_c93208 _d93208