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Exercises In Probability

Author: L. Chaumont
Publisher: Cambridge University Press
ISBN: 9780521825856
Size: 54.81 MB
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This book was first published in 2003. Derived from extensive teaching experience in Paris, this book presents around 100 exercises in probability. The exercises cover measure theory and probability, independence and conditioning, Gaussian variables, distributional computations, convergence of random variables, and random processes. For each exercise the authors have provided detailed solutions as well as references for preliminary and further reading. There are also many insightful notes to motivate the student and set the exercises in context. Students will find these exercises extremely useful for easing the transition between simple and complex probabilistic frameworks. Indeed, many of the exercises here will lead the student on to frontier research topics in probability. Along the way, attention is drawn to a number of traps into which students of probability often fall. This book is ideal for independent study or as the companion to a course in advanced probability theory.

Exercises In Probability

Author: Loïc Chaumont
Publisher: Cambridge University Press
ISBN: 1107606551
Size: 16.83 MB
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Over 100 exercises with detailed solutions, insightful notes and references for further reading. Ideal for beginning researchers.

Spatial Branching In Random Environments And With Interaction

Author: Englander Janos
Publisher: World Scientific
ISBN: 9814569852
Size: 16.60 MB
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This unique volume discusses some recent developments in the theory of spatial branching processes and superprocesses, with special emphasis on spines, Laws of Large Numbers, interactions and random media.Although this book is mainly written for mathematicians, the models discussed are relevant to certain models in population biology, and are thus hopefully interesting to the applied mathematician/biologist as well.The necessary background material in probability and analysis is provided in a comprehensive introductory chapter. Historical notes and several exercises are provided to complement each chapter.

Option Prices As Probabilities

Author: Christophe Profeta
Publisher: Springer Science & Business Media
ISBN: 9783642103957
Size: 32.55 MB
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Discovered in the seventies, Black-Scholes formula continues to play a central role in Mathematical Finance. We recall this formula. Let (B ,t? 0; F ,t? 0, P) - t t note a standard Brownian motion with B = 0, (F ,t? 0) being its natural ?ltra- 0 t t tion. Let E := exp B? ,t? 0 denote the exponential martingale associated t t 2 to (B ,t? 0). This martingale, also called geometric Brownian motion, is a model t to describe the evolution of prices of a risky asset. Let, for every K? 0: + ? (t) :=E (K?E ) (0.1) K t and + C (t) :=E (E?K) (0.2) K t denote respectively the price of a European put, resp. of a European call, associated with this martingale. Let N be the cumulative distribution function of a reduced Gaussian variable: x 2 y 1 ? 2 ? N (x) := e dy. (0.3) 2? ?? The celebrated Black-Scholes formula gives an explicit expression of? (t) and K C (t) in terms ofN : K ? ? log(K) t log(K) t ? (t)= KN ? + ?N ? ? (0.4) K t 2 t 2 and ? ?

S Minaire De Probabilit S Xlii

Author: Catherine Donati-Martin
Publisher: Springer
ISBN: 3642017630
Size: 14.49 MB
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This book offers an introduction to rough paths. Coverage also includes the interface between analysis and probability to special processes, Lévy processes and Lévy systems, representation of Gaussian processes, filtrations and quantum probability.