Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Books
  3. Exercises in Probability
  • Cited by 7
  • 2nd edition
  • Loïc Chaumont, Université d'Angers, France, Marc Yor, Université de Paris VI (Pierre et Marie Curie)
Publisher:
Cambridge University Press
Online publication date:
August 2012
Print publication year:
2012
Online ISBN:
9781139135351
DOI:
https://doi.org/10.1017/CBO9781139135351
Series:
Cambridge Series in Statistical and Probabilistic Mathematics (35)
Subjects:
Probability Theory and Stochastic Processes, General Statistics and Probability, Statistics and Probability
Information

Book description

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. 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.

Reviews

‘In conclusion, this is an excellent book, which should be in every library, and also on the bookshelf of anyone with interests in advanced probability and random processes.'

Source: Society for Industrial and Applied Mathematics

‘… extremely useful for graduate and postgraduate students and those who want to better understand advanced probability theory.'

Source: European Mathematical Society Newsletter

‘… although the book could profitably be used as a companion to a graduate course in probability theory, it is probably best designed for the doctoral student who can read it alongside the source material. Used in that way, the book is a magnificent resource … consistency and clarity of mathematical style … For beginning researchers in stochastic mathematics, this book comes highly recommended and libraries should obtain a copy.'

Source: Journal of the Royal Statistical Society: Series A

‘This book, written in an inspiring style, can be used together with almost any advanced course and strongly recommend to doctoral and master students in the area of probability and stochastic processes. Young researchers and university teachers as well as professionals can benefit a lot from this book.'

Jordan M. Stoyanov Source: Zentralblatt MATH

Refine List

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

Contents

Contents
References
References
References
[1] G.E., Andrews, R., Askey and R., Roy: Special Functions. Encyclopedia of Mathematics and its Applications, 71. Cambridge University Press, Cambridge, 1999.
[2] P., Baldi, L., Mazliak and P., Priouret: Martingales et Chaînes de Markov. Collection Méthodes, Hermann, 1998. English version: Chapman & Hall/CRC, Oxford, 2002.
[3] Ph., Barbe and M., Ledoux: Probabilité. De la Licence à l'Agrégation. Éditions Espaces 34, Belin, 1998.
[4] O.E., Barndorff-Nielsen and A., Shiryaev: Change of Time and Change of Measure. Advanced Series on Statistical Science & Applied Probability, 13. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2010.
[5] J., Bertoin: Lévy Processes. Cambridge University Press, Cambridge, 1996.
[6] P., Billingsley: Convergence of Probability Measures. Second edition. John Wiley & Sons, Inc., New York, 1999.
[7] P., Billingsley: Probability and Measure. Third edition. John Wiley & Sons, Inc., New York, 1995.
[8] P., Billingsley: Ergodic Theory and Information. Reprint of the 1965 original. Robert E. Krieger Publishing Co., Huntington, NY, 1978.
[9] N.H., Bingham, C.M., Goldie and J.L., Teugels: Regular Variation. Cambridge University Press, Cambridge, 1989.
[10] A.N., Borodin and P., Salminen: Handbook of Brownian Motion – Facts and Formulae. Second edition. Probability and its Applications. Birkhäuser Verlag, Basel, 2002. Third edition in preparation (September 2011).
[11] M., Brancovan and Th., Jeulin: Probabilités – Niveau M1, Vol. 2, Ellipses, in preparation (September 2011).
[12] M., Brancovan and Th., Jeulin: Probabilités – Niveau M1, Ellipses, 2006.
[13] L., Breiman: Probability. Addison-Wesley Publishing Company, Reading, Mass.-London-Don Mills, Ont., 1968.
[14] P., Brémaud: An Introduction to Probabilistic Modeling. Corrected reprint of the 1988 original. Springer-Verlag, New York, 1994.
[15] L., Chaumont: An Introduction to Self-similar Processes. In preparation (March 2012).
[16] Y.S., Chow and H., Teicher: Probability Theory. Independence, Interchangeability, Martingales. Third edition. Springer-Verlag, New York, 1997.
[17] K.L., Chung: A Course in Probability Theory. Third edition. Academic Press, Inc., San Diego, CA, 2001.
[18] E., Çinlar: Probability and Stochastics. Graduate Texts in Mathematics, 261. Springer, New York, 2011.
[19] D., Dacunha-Castelle, M., Duflo and V., Genon-Catalot: Exercices de Probabilités et Statistiques. Tome 2. Problèmes à temps mobile. Masson, 1984.
[20] D., Dacunha-Castelle and M., Duflo: Probabilités et Statistiques. Tome 2. Problèmes à temps mobile. Masson, Paris, 1983.
[21] D., Dacunha-Castelle and M., Duflo: Probabilités et Statistiques. Tome 1. Problèmes à temps fixe. Masson, Paris, 1982.
[22] D., Dacunha-Castelle, D., Revuz and M., Schreiber: Recueil de Problèmes de Calcul des Probabilités. Deuxième édition. Masson, Paris, 1970.
[23] C., Dellacherie and P.A., Meyer: Probabilités et Potentiel. Chapitres I à IV. Hermann, Paris, 1975.
[24] J.L., Doob: Stochastic Processes. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1990.
[25] A.Y., Dorogovtsev, D.S., Silvestrov, A.V., Skorokhod and M.I., Yadrenko: Probability Theory: Collection of Problems. Translations of Mathematical Monographs, 163. American Mathematical Society, Providence, RI, 1997.
[26] R., Durrett: Probability: Theory and Examples. Fourth edition. Cambridge University Press, Cambridge, 2010.
[27] P., Embrechts and M., Maejima: Selfsimilar Processes. Princeton University Press, Princeton, NJ, 2002.
[28] W., Feller: An Introduction to Probability Theory and its Applications. Vol. II. Second edition. John Wiley & Sons, Inc., New York–London–Sydney, 1971.
[29] X., Fernique: Fonctions Aléatoires Gaussiennes, Vecteurs Aléatoires Gaussiens. Université de Montréal, Centre de Recherches Mathématiques, Montréal, QC, 1997.
[30] D., Foata and A., Fuchs: Processus Stochastiques, Processus de Poisson, Chaînes de Markov et Martingales. Cours et exercices corrigés. Dunod, Paris, 2002.
[31] D., Foata and A., Fuchs: Calcul des Probabilités. Second edition. Dunod, 1998.
[32] D., Freedman: Brownian Motion and Diffusion. Second edition. Springer-Verlag, New York–Berlin, 1983.
[33] B., Fristedt and L., Gray: A Modern Approach to Probability Theory. Probability and its applications. Birkhäuser Boston, Inc., Boston, MA, 1997.
[34] L., Gallardo: Mouvement Brownien et Calcul d'Itô – Cours et Exercices Corrigés. Hermann, 2008.
[35] H.-O., Georgii: Gibbs Measures and Phase Transitions. Second edition. de Gruyter Studies in Mathematics, 9. Walter de Gruyter & Co., Berlin, 2011.
[36] G.R., Grimmett: Probability on Graphs. Random Processes on Graphs and Lattices. Cambridge University Press, Cambridge, 2010.
[37] G.R., Grimmett and D.R. S, tirzaker: One Thousand Exercises in Probability. The Clarendon Press, Oxford University Press, New York, 2001.
[38] G.R., Grimmett and D.R., Stirzaker: Probability and Random Processes. Second edition. The Clarendon Press, Oxford University Press, New York, 1992.
[39] T., Hida and M., Hitsuda: Gaussian processes. Translations of Mathematical Monographs, 120. American Mathematical Society, Providence, RI, 1993.
[40] J., Jacod and Ph., Protter: Probability Essentials. Second edition. Universitext. Springer-Verlag, Berlin, 2002.
[41] S., Janson: Gaussian Hilbert Spaces. Cambridge Tracts in Mathematics, 129. Cambridge University Press, Cambridge, 1997.
[42] N.L., Johnson, S., Kotz and N., Balakrishnan: Continuous Univariate Distributions. Vol. 2. Second edition. John Wiley & Sons, Inc., New York, 1995.
[43] M., Kac: Statistical Independence in Probability, Analysis and Number Theory. The Carus Mathematical Monographs, No. 12. Distributed by John Wiley and Sons, Inc., New York 1959.
[44] O., Kallenberg: Foundations of Modern Probability. Second edition. Probability and its Applications. Springer-Verlag, New York, 2002.
[45] G., Kallianpur: Stochastic Filtering Theory. Applications of Mathematics, 13. Springer-Verlag, New York-Berlin, 1980.
[46] I., Karatzas and S.N., Shreve: Brownian Motion and Stochastic Calculus. Second edition. Springer-Verlag, New York, 1991.
[47] D., Khoshnevisan: Probability. Graduate Studies in Mathematics, 80. American Mathematical Society, Providence, RI, 2007.
[48] A., Klenke: Probability Theory. A Comprehensive Course. Springer-Verlag, London, Ltd., London, 2008.
[49] A.N., Kolmogorov: Foundations of the Theory of Probability. Chelsea Publishing Company, New York, 1950.
[50] M., Ledoux and M., Talagrand: Probability in Banach Spaces. Isoperimetry and Processes. Results in Mathematics and Related Areas (3), 23. Springer-Verlag, Berlin, 1991.
[51] N.N., Lebedev: Special Functions and their Applications. Unabridged and corrected republication. Dover Publications, Inc., New York, 1972.
[52] G., Letac: Exercises and Solutions Manual for Integration and Probability. Springer-Verlag, New York, 1995. French edition: Masson, Second edition, 1997.
[53] M.A., Lifschits: Gaussian Random Functions. Kluwer Academic Publishers, 1995.
[54] T.M., Liggett: Continuous Time Markov Processes. An Introduction. Graduate Studies in Mathematics, 113. American Mathematical Society, Providence, RI, 2010.
[55] E., Lukacs: Developments in Characteristic Function Theory. Macmillan Co., New York, 1983.
[56] H.P., Mc Kean: Stochastic Integrals. Reprint of the 1969 edition, with errata. AMS Chelsea Publishing, Providence, RI, 2005.
[57] P., Malliavin and H., Airault: Integration and Probability. Graduate Texts in Mathematics, 157. Springer-Verlag, New York, 1995. French edition: Masson, 1994.
[58] R., Mansuy and M., Yor: Aspects of Brownian Motion. Universitext. Springer-Verlag, Berlin, 2008.
[59] S., Méléard: Aléatoire. Introduction à la Théorie et au Calcul des Probabilités. Éditions de l'École Polytechnique, 2010.
[60] P.A., Meyer: Probability and Potentials. Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.–Toronto, Ont.–London, 1966. French edition: Herman (1966).
[61] P., Mörters and Y., Peres: Brownian Motion. With an Appendix by Oded Schramm and Wendelin Werner. Cambridge University Press, Cambridge, 2010.
[62] J., Neveu: Discrete-parameter Martingales. Revised edition. North-Holland Mathematical Library, Vol. 10., Amsterdam–Oxford–New York, 1975.
[63] J., Neveu: Mathematical Foundations of the Calculus of Probability. Holden-Day, Inc., 1965. French edition: Masson, Second edition, 1970.
[64] J., Neveu: Processus Aléatoires Gaussiens. Séminaire de Mathématiques Supérieures, No. 34. Les Presses de l'Université de Montréal, 1968.
[65] B., Øksendal: Stochastic Differential Equations. An Introduction with Applications. Sixth edition. Universitext. Springer-Verlag, Berlin, 2003.
[66] S.J., Patterson: An Introduction to the Theory of the Riemann Zetafunction. Cambridge Studies in Advanced Mathematics, 14. Cambridge University Press, Cambridge, 1988.
[67] K., Petersen: Ergodic Theory. Cambridge Studies in Advanced Mathematics 2. Cambridge University Press, Cambridge, 1983.
[68] V.V., Petrov: Limit Theorems of Probability Theory. Sequences of Independent Random Variables. Oxford University Press, New York, 1995.
[69] J., Pitman: Probability. Springer-Verlag, 1993.
[70] Ch., Profeta, B., Roynette and M., Yor: Option Prices as Probabilities. A New Look at Generalized Black–Scholes Formulae. Springer Finance. Springer-Verlag, Berlin, 2010.
[71] P.E., Protter: Stochastic Integration and Differential Equations. Second edition. Applications of Mathematics, 21. Springer-Verlag, Berlin, 2004.
[72] A., Rényi: Calcul des Probabilités. Collection Universitaire de Mathématiques, No. 21, Dunod, Paris, 1966.
[73] D., Revuz: Probabilités. Hermann, Paris, 1998.
[74] D., Revuz: Intégration. Hermann, Paris, 1997.
[75] D., Revuz and M., Yor: Continuous Martingales and Brownian Motion. Third edition. Springer-Verlag, Berlin, 1999.
[76] L.C.G., Rogers and D., Williams: Diffusions, Markov Processes, and Martingales. Vol. 1. Foundations. Reprint of the second (1994) edition. Cambridge Mathematical Library. Cambridge University Press, Cambridge, 2000.
[77] L.C.G., Rogers and D., Williams: Diffusions, Markov Processes, and Martingales. Vol. 2. Itô Calculus. Second edition. Cambridge University Press, Cambridge, 2000.
[78] J.P., Romano and A.F., Siegel: Counterexamples in Probability and Statistics. Wadsworth & Brooks/Cole Advanced Books & Software, Monterey, CA, 1986.
[79] S.M., Ross: Stochastic Processes. Second edition. John Wiley & Sons, Inc., New York, 1996.
[80] G., Samorodnitsky and M.S., Taqqu: Stable Non-Gaussian Random Processes. Chapman & Hall, New York, 1994.
[81] K., Sato: Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press, Cambridge, 1999.
[82] A.N., Shiryaev: Probability. Second edition. Graduate Texts in Mathematics, 95. Springer-Verlag, New York, 1996.
[83] Y.G., Sinaï: Probability Theory. An Introductory Course. Springer-Verlag, Berlin, 1992.
[84] A.V., Skorokhod: Basic Principles and Applications of Probability Theory. Springer-Verlag, Berlin, 2005.
[85] F.W., Steutel and K., van Harn: Infinite Divisibility of Probability Distributions on the Real Line. Monographs and Textbooks in Pure and Applied Mathematics, 259. Marcel Dekker, Inc., New York, 2004.
[86] J.M., Stoyanov: Counterexamples in Probability. Second edition. Wiley Series in Probability and Mathematical Statistics. John Wiley & Sons, Ltd., Chichester, 1997.
[87] D.W., Stroock: Probability Theory, an Analytic View. Second edition. Cambridge University Press, Cambridge, 2011.
[88] D.W., Stroock: Partial Differential Equations for Probabilists. Cambridge Studies in Advanced Mathematics, 112. Cambridge University Press, Cambridge, 2008.
[89] D.W., Stroock: Markov Processes from K. Itô's Perspective. Annals of Mathematics Studies, 155, Princeton University Press, Princeton, NJ, 2003.
[90] G.J, Székely: Paradoxes in Probability Theory and Mathematical Statistics. Mathematics and its Applications (East European Series), 15. D. Reidel Publishing Co., Dordrecht, 1986.
[91] M., Talagrand: Mean Field Models For Spin Glasses. Volume I. Basic examples. 54. Springer-Verlag, Berlin, 2011.
[92] M., Talagrand: Spin Glasses: a Challenge for Mathematicians. Cavity and Mean Field Models. Results in Mathematics and Related Areas. 3rd Series, 46. Springer-Verlag, Berlin, 2003.
[93] P.S., Toulouse: Thèmes de Probabilités et Statistiques. Agrégation de Mathématiques. Dunod, 1999.
[94] V.V., Uchaikin and V.M., Zolotarev: Chance and Stability. Stable Distributions and their Applications. Modern Probability and Statistics. VSP, Utrecht, 1999.
[95] P., Whittle: Probability via Expectation. Fourth edition. Springer Texts in Statistics. Springer-Verlag, New York, 2000.
[96] D.V., Widder: The Laplace Transform. Princeton Mathematical Series, v. 6. Princeton University Press, Princeton, NJ, 1941.
[97] D., Williams: Weighing the Odds. A Course in Probability and Statistics. Cambridge University Press, Cambridge, 2001.
[98] D., Williams: Probability with Martingales. Cambridge Mathematical Textbooks. Cambridge University Press, Cambridge, 1991.
[99] D., Williams: Diffusions, Markov Processes, and Martingales. Vol. 1. Foundations. Probability and Mathematical Statistics. John Wiley & Sons, Ltd., Chichester, 1979.
[100] M., Yor: Small and Big Probability Worlds. Banach Center Publications, Vol. 95, Institute of Mathematics Polish Academy of Sciences Warszawa, 2011, pp. 261–271.
[101] M., Yor: Some Aspects of Brownian Motion, Part I. Some special functionals. Lectures in Mathematics ETH Zürich. Birkhäuser Verlag, Basel, 1992.
[102] M., Yor, M.E., Vares and T., Mikosch: A tribute to Professor Kiyosi Itô. Stochastic Process. Appl., 120 (2010), no. 1, 1.
[103] V.M., Zolotarev: One-dimensional Stable Distributions. Translations of Mathematical Monographs, 65. American Mathematical Society, Providence, RI, 1986.

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Book summary page views

Total views: 0 *
Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.