000			03642nam a22004335i 4500
001			978-0-387-31057-2
003			DE-He213
005			20250710083947.0
007			cr nn 008mamaa
008			100301s2006 xxu| s |||| 0|eng d
020			_a9780387310572 _a99780387310572
024	7		_a10.1007/0-387-31057-6 _2doi
082	0	4	_a519.2 _223
100	1		_aKuo, Hui-Hsiung. _eauthor.
245	1	0	_aIntroduction to Stochastic Integration _h[recurso electrónico] / _cby Hui-Hsiung Kuo.
264		1	_aNew York, NY : _bSpringer New York, _c2006.
300			_aXIII, 279 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aUniversitext
505	0		_aBrownian Motion -- Constructions of Brownian Motion -- Stochastic Integrals -- An Extension of Stochastic Integrals -- Stochastic Integrals for Martingales -- The Itô Formula -- Applications of the Itô Formula -- Multiple Wiener-Itô Integrals -- Stochastic Differential Equations -- Some Applications and Additional Topics.
520			_aThe theory of stochastic integration, also called the Ito calculus, has a large spectrum of applications in virtually every scientific area involving random functions, but it can be a very difficult subject for people without much mathematical background. The Ito calculus was originally motivated by the construction of Markov diffusion processes from infinitesimal generators. Previously, the construction of such processes required several steps, whereas Ito constructed these diffusion processes directly in a single step as the solutions of stochastic integral equations associated with the infinitesimal generators. Moreover, the properties of these diffusion processes can be derived from the stochastic integral equations and the Ito formula. This introductory textbook on stochastic integration provides a concise introduction to the Ito calculus, and covers the following topics: * Constructions of Brownian motion; * Stochastic integrals for Brownian motion and martingales; * The Ito formula; * Multiple Wiener-Ito integrals; * Stochastic differential equations; * Applications to finance, filtering theory, and electric circuits. The reader should have a background in advanced calculus and elementary probability theory, as well as a basic knowledge of measure theory and Hilbert spaces. Each chapter ends with a variety of exercises designed to help the reader further understand the material. Hui-Hsiung Kuo is the Nicholson Professor of Mathematics at Louisiana State University. He has delivered lectures on stochastic integration at Louisiana State University, Cheng Kung University, Meijo University, and University of Rome "Tor Vergata," among others. He is also the author of Gaussian Measures in Banach Spaces (Springer 1975), and White Noise Distribution Theory (CRC Press 1996), and a memoir of his childhood growing up in Taiwan, An Arrow Shot into the Sun (Abridge Books 2004).
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: _z9780387287201
830		0	_aUniversitext
856	4	0	_uhttp://dx.doi.org/10.1007/0-387-31057-6 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c57097 _d57097