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Exercises in probability : a guided tour from measure theory to random processes, via conditioning /
"Derived from extensive teaching experience in Paris, this second edition now includes over 100 exercises in probability. New exercises have been added to reflect important areas of current research in probability theory, including infinite divisibility of stochastic processes, past-future mart...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2012.
|
| Edición: | 2nd ed. |
| Colección: | Cambridge series on statistical and probabilistic mathematics.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Chaumont, L. |q (Loïc) | |
| 245 | 1 | 0 | |a Exercises in probability : |b a guided tour from measure theory to random processes, via conditioning / |c Loïc Chaumont, Marc Yor. |
| 250 | |a 2nd ed. | ||
| 260 | |a Cambridge : |b Cambridge University Press, |c 2012. | ||
| 300 | |a 1 online resource (xx, 279 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
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| 490 | 1 | |a Cambridge series in statistical and probabilistic mathematics | |
| 520 | |a "Derived from extensive teaching experience in Paris, this second edition now includes over 100 exercises in probability. New exercises have been added to reflect important areas of current research in probability theory, including infinite divisibility of stochastic processes, past-future martingales and fluctuation theory. For each exercise the authors provide 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"-- |c Provided by publisher | ||
| 504 | |a Includes bibliographical references (pages 270-277) and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Preface to the Second Edition -- Preface to the First Edition -- 1. Measure theory and probability -- 2. Independence and conditioning -- 3. Gaussian variables -- 4. Distributional computations -- 5. Convergence of random variables -- 6. Random processes -- Where is the notion N discussed? -- Final suggestions: how to go further? | |
| 546 | |a English. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Probabilities. | |
| 650 | 0 | |a Probabilities |v Problems, exercises, etc. | |
| 650 | 2 | |a Probability | |
| 650 | 4 | |a Mathematics. | |
| 650 | 4 | |a Probabilities |v Problems, exercises, etc. | |
| 650 | 6 | |a Probabilités. | |
| 650 | 6 | |a Probabilités |v Problèmes et exercices. | |
| 650 | 7 | |a probability. |2 aat | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x General. |2 bisacsh | |
| 650 | 7 | |a Probabilities. |2 fast |0 (OCoLC)fst01077737 | |
| 655 | 2 | |a Problems and Exercises | |
| 655 | 7 | |a exercise books. |2 aat | |
| 655 | 7 | |a Problems and exercises. |2 fast |0 (OCoLC)fst01423783 | |
| 655 | 7 | |a Problems and exercises. |2 lcgft | |
| 655 | 7 | |a Problèmes et exercices. |2 rvmgf | |
| 700 | 1 | |a Yor, Marc. | |
| 776 | 0 | 8 | |i Print version: |a Chaumont, L. (Loïc). |t Exercises in probability. |b 2nd ed. |d Cambridge ; New York : Cambridge University Press, 2012 |z 9781107606555 |w (DLC) 2012002653 |w (OCoLC)773921342 |
| 830 | 0 | |a Cambridge series on statistical and probabilistic mathematics. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=466664 |z Texto completo |
| 880 | 0 | |6 505-00/(S |a Cover -- Exercises in Probability -- Series -- Title -- Copyright -- Dedication -- Contents -- Preface to the second edition -- Preface to the first edition -- Some frequently used notations -- Chapter 1: Measure theory and probability -- 1.1 Some traps concerning the union of σ-fields -- 1.2 Sets which do not belong in a strong sense, to a σ-field -- 1.3 Some criteria for uniform integrability -- 1.4 When does weak convergence imply the convergence of expectations-- 1.5 Conditional expectation and the Monotone Class Theorem -- 1.6 Lp-convergence of conditional expectations -- 1.7 Measure preserving transformations -- 1.8 Ergodic transformations -- 1.9 Invariant σ-fields -- 1.10 Extremal solutions of (general) moments problems -- 1.11 The log normal distribution is moments indeterminate -- 1.12 Conditional expectations and equality in law -- 1.13 Simplifiable random variables -- 1.14 Mellin transform and simplification -- 1.15 There exists no fractional covering of the real line -- Solutions for Chapter 1 -- Solution to Exercise 1.1 -- Solution to Exercise 1.2 -- Solution to Exercise 1.3 -- Solution to Exercise 1.4 -- Solution to Exercise 1.5 -- Solution to Exercise 1.6 -- Solution to Exercise 1.7 -- Solution to Exercise 1.8 -- Solution to Exercise 1.9 -- Solution to Exercise 1.10 -- Solution to Exercise 1.11 -- Solution to Exercise 1.12 -- Solution to Exercise 1.13 -- Solution to Exercise 1.14 -- Solution to Exercise 1.15 -- Chapter 2: Independence and conditioning -- 2.1 Independence does not imply measurability with respect to an independent complement -- 2.2 Complement to Exercise 2.1: further statements of independence versus measurability -- 2.3 Independence and mutual absolute continuity -- 2.4 Size-biased sampling and conditional laws -- 2.5 Think twice before exchanging the order of taking the supremum and intersection of σ-fields! | |
| 880 | 8 | |6 505-00/(S |a 2.6 Exchangeability and conditional independence: de Finetti's theorem -- 2.7 On exchangeable σ-fields -- 2.8 Too much independence implies constancy -- 2.9 A double paradoxical inequality -- 2.10 Euler's formula for primes and probability -- 2.11 The probability, for integers, of being relatively prime -- 2.12 Completely independent multiplicative sequences of U-valued random variables -- 2.13 Bernoulli random walks considered at some stopping time -- 2.14 cosh, sinh, the Fourier transform and conditional independence -- 2.15 cosh, sinh, and the Laplace transform -- 2.16 Conditioning and changes of probabilities -- 2.17 Radon-Nikodym density and the Acceptance- Rejection Method of von Neumann -- 2.18 Negligible sets and conditioning -- 2.19 Gamma laws and conditioning -- 2.20 Random variables with independent fractional and integer parts -- 2.21 Two characterizations of the simple random walk -- Solutions for Chapter 2 -- Solution to Exercise 2.1 -- Solution to Exercise 2.2 -- Solution to Exercise 2.3 -- Solution to Exercise 2.4 -- Solution to Exercise 2.5 -- Solution to Exercise 2.6 -- Solution to Exercise 2.7 -- Solution to Exercise 2.8 -- Solution to Exercise 2.9 -- Solution to Exercise 2.10 -- Solution to Exercise 2.11 -- Solution to Exercise 2.12 -- Solution to Exercise 2.13 -- Solution to Exercise 2.14 -- Solution to Exercise 2.15 -- Solution to Exercise 2.16 -- Solution to Exercise 2.17 -- Solution to Exercise 2.18 -- Solution to Exercise 2.19 -- Solution to Exercise 2.20 -- Solution to Exercise 2.21 -- Chapter 3: Gaussian variables -- 3.1 Constructing Gaussian variables from, but not belonging to, a Gaussian space -- 3.2 A complement to Exercise 3.1 -- 3.3 Gaussian vectors and orthogonal projections -- 3.4 On the negative moments of norms of Gaussian vectors -- 3.5 Quadratic functionals of Gaussian vectors and continued fractions. | |
| 880 | 8 | |6 505-00/(S |a 5.11 Convergence in law of stable(μ) variables, as μτ̔̈"»9"·0 -- 5.12 Finite-dimensional convergence in law towards Brownian motion -- 5.13 The empirical process and the Brownian bridge -- 5.14 The functional law of large numbers -- 5.15 The Poisson process and Brownian motion -- 5.16 Brownian bridges converging in law to Brownian motions -- 5.17 An almost sure convergence result for sums of stable random variables -- Chapter 6: Random processes -- 6.1 Jeulin's lemma deals with the absolute convergence of integrals of random processes -- 6.2 Functions of Brownian motion as solutions to SDEs -- the example of (x) = sinh(x) -- 6.3 Bougerol's identity and some Bessel variants -- 6.4 Doléans-Dade exponentials and the Maruyama- Girsanov-Van Schuppen-Wong theorem revisited -- 6.5 The range process of Brownian motion -- 6.6 Symmetric Lévy processes reflected at their minimum and maximum -- E. Csáki's formulae for the ratio of Brownian extremes -- 6.7 Infinite divisibility with respect to time -- 6.8 A toy example for Westwater's renormalization -- 6.9 Some asymptotic laws of planar Brownian motion -- 6.10 Windings of the three-dimensional Brownian motion around a line -- 6.11 Cyclic exchangeability property and uniform law related to the Brownian bridge -- 6.12 Local time and hitting time distributions for the Brownian bridge -- 6.13 Partial absolute continuity of the Brownian bridge distribution with respect to the Brownian distribution -- 6.14 A Brownian interpretation of the duplication formula for the gamma function -- 6.15 Some deterministic time-changes of Brownian motion -- 6.16 A new path construction of Brownian and Bessel bridges -- 6.17 Random scaling of the Brownian bridge -- 6.18 Time-inversion and quadratic functionals of Brownian motion -- Lévy's stochastic area formula -- 6.19 Quadratic variation and local time of semimartingales. | |
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