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Aspects of Brownian Motion

By: Mansuy, Roger [author.].
Contributor(s): Yor, Marc [author.] | SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Universitext: Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.Description: XIV, 200 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783540499664.Subject(s): Mathematics | Probabilities | Mathematics | Probability Theory and Stochastic ProcessesDDC classification: 519.2 Online resources: Click here to access online
Contents:
The Gaussian space of BM -- The laws of some quadratic functionals of BM -- Squares of Bessel processes and Ray-Knight theorems for Brownian local times -- An explanation and some extensions of the Ciesielski-Taylor identities -- On the winding number of planar BM -- On some exponential functionals of Brownian motion and the problem of Asian options -- Some asymptotic laws for multidimensional BM -- Some extensions of Paul Lévy’s arc sine law for BM -- Further results about reflecting Brownian motion perturbed by its local time at 0 -- On principal values of Brownian and Bessel local times -- Probabilistic representations of the Riemann zeta function and some generalisations related to Bessel processes.
In: Springer eBooksSummary: Stochastic calculus and excursion theory are very efficient tools to obtain either exact or asymptotic results about Brownian motion and related processes. The emphasis of this book is on special classes of such Brownian functionals as: - Gaussian subspaces of the Gaussian space of Brownian motion; - Brownian quadratic funtionals; - Brownian local times, - Exponential functionals of Brownian motion with drift; - Winding number of one or several Brownian motions around one or several points or a straight line, or curves; - Time spent by Brownian motion below a multiple of its one-sided supremum. Besides its obvious audience of students and lecturers the book also addresses the interests of researchers from core probability theory out to applied fields such as polymer physics and mathematical finance.
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Item type Current location Call number Status Date due Barcode Item holds
E books E books PK Kelkar Library, IIT Kanpur
Available EBK10361
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The Gaussian space of BM -- The laws of some quadratic functionals of BM -- Squares of Bessel processes and Ray-Knight theorems for Brownian local times -- An explanation and some extensions of the Ciesielski-Taylor identities -- On the winding number of planar BM -- On some exponential functionals of Brownian motion and the problem of Asian options -- Some asymptotic laws for multidimensional BM -- Some extensions of Paul Lévy’s arc sine law for BM -- Further results about reflecting Brownian motion perturbed by its local time at 0 -- On principal values of Brownian and Bessel local times -- Probabilistic representations of the Riemann zeta function and some generalisations related to Bessel processes.

Stochastic calculus and excursion theory are very efficient tools to obtain either exact or asymptotic results about Brownian motion and related processes. The emphasis of this book is on special classes of such Brownian functionals as: - Gaussian subspaces of the Gaussian space of Brownian motion; - Brownian quadratic funtionals; - Brownian local times, - Exponential functionals of Brownian motion with drift; - Winding number of one or several Brownian motions around one or several points or a straight line, or curves; - Time spent by Brownian motion below a multiple of its one-sided supremum. Besides its obvious audience of students and lecturers the book also addresses the interests of researchers from core probability theory out to applied fields such as polymer physics and mathematical finance.

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