Exercises in Probability: A Guided Tour from Measure Theory to Random Processes, via Conditioning

1. Measure theory and probability 2. Independence and conditioning 3. Gaussian variables 4. Distributional computations 5. Convergence of random variables 6. Random processes.

[1]  D. Widder,et al.  The Laplace Transform , 1943, The Mathematical Gazette.

[2]  David Stirzaker,et al.  One Thousand Exercises in Probability , 2001 .

[3]  Ken-iti Sato.  Lévy Processes and Infinitely Divisible Distributions , 1999 .

[4]  David S. Williams.  Weighing the odds : a course in probability and statistics , 2001 .

[5]  N. L. Johnson,et al.  Continuous Univariate Distributions. , 1995 .

[6]  G. Grimmett,et al.  Probability and random processes , 2002 .

[7]  A. Borodin,et al.  Handbook of Brownian Motion - Facts and Formulae , 1996 .

[8]  M. Kac.  Statistical Independence in Probability Analysis and Number Theory , 1959 .

[9]  Jordan Stoyanov,et al.  Counterexamples in Probability , 1988 .

[10]  I︠u︡. V. Prokhorov,et al.  Basic Principles and Applications of Probability Theory , 2004 .

[11]  D. Lindley,et al.  Paradoxes in Probability Theory and Mathematical Statistics , 1987 .

[12]  H. Teicher,et al.  Probability theory: Independence, interchangeability, martingales , 1978 .

[13]  Paul Malliavin,et al.  Integration and Probability , 1995, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[14]  O. Kallenberg.  Foundations of Modern Probability , 2021, Probability Theory and Stochastic Modelling.

[15]  M. Yor.  Some Aspects Of Brownian Motion , 1992 .

[16]  P. Protter.  Stochastic integration and differential equations , 1990 .

[17]  Eric R. Ziegel,et al.  Counterexamples in Probability and Statistics , 1986 .

[18]  S. Janson.  Gaussian Hilbert Spaces , 1997 .

[19]  L. Rogers,et al.  Diffusions, Markov processes, and martingales , 1979 .

[20]  Kai Lai Chung,et al.  A Course in Probability Theory , 1949 .

[21]  J. Doob.  Stochastic processes , 1953 .

[22]  R. A. Silverman,et al.  Special functions and their applications , 1966 .

[23]  V. V. Petrov.  Limit Theorems of Probability Theory: Sequences of Independent Random Variables , 1995 .

[24]  Eugene Lukacs,et al.  Developments in Characteristic Function Theory , 1976 .

[25]  M. Talagrand.  Spin glasses : a challenge for mathematicians : cavity and mean field models , 2003 .

[26]  Peter Whittle,et al.  Probability via expectation , 1992 .

[27]  J. Neveu,et al.  Processus aléatoires gaussiens , 1968 .

[28]  M. Lifshits.  Gaussian Random Functions , 1995 .

[29]  F. Steutel,et al.  Infinite Divisibility of Probability Distributions on the Real Line , 2003 .

[30]  Gérard Letac,et al.  Exercises and Solutions Manual for Integration and Probability: By Paul Malliavin , 1995 .

[31]  J. Neveu,et al.  Discrete Parameter Martingales , 1975 .

[32]  J. Neveu,et al.  Mathematical foundations of the calculus of probability , 1965 .

[33]  Gábor J. Székely,et al.  Paradoxes in Probability Theory and Mathematical Statistics , 1987 .

[34]  P. Billingsley,et al.  Convergence of Probability Measures , 1969 .

[35]  A. N. Kolmogorov,et al.  Foundations of the theory of probability , 1960 .

[36]  P. Brémaud.  An Introduction to Probabilistic Modeling , 1994 .

[37]  G. Kallianpur.  Stochastic Filtering Theory , 1980 .

[38]  M. Talagrand,et al.  Probability in Banach Spaces: Isoperimetry and Processes , 1991 .

[39]  Karl Petersen.  Ergodic Theory , 1983 .

[40]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[41]  R. Durrett.  Probability: Theory and Examples , 1993 .

[42]  D. Applebaum.  Stable non-Gaussian random processes , 1995, The Mathematical Gazette.

[43]  V. Zolotarev.  One-dimensional stable distributions , 1986 .

[44]  Ioannis Karatzas,et al.  Brownian Motion and Stochastic Calculus , 1987 .

[45]  Hans-Otto Georgii,et al.  Gibbs Measures and Phase Transitions , 1988 .

[46]  S. J. Patterson,et al.  An Introduction to the theory of the Riemann zeta-function: Contents , 1988 .

[47]  M. Yor,et al.  Continuous martingales and Brownian motion , 1990 .

[48]  D. Nualart.  GAUSSIAN HILBERT SPACES (Cambridge Tracts in Mathematics 129) By SVANTE JANSON: 340 pp., £40.00, ISBN 0 521 56128 0 (Cambridge University Press, 1997) , 1998 .

[49]  Paolo Baldi,et al.  Martingales et chaînes de Markov , 1998 .

[50]  Philip Sedgwick,et al.  Probability Theory: An Introductory Course , 1992 .

[51]  Didier Dacunha-Castelle,et al.  Recueil de problèmes de calcul des probabilités , 1965 .

[52]  A. I︠a︡. Dorogovt︠s︡ev.  Probability Theory: Collection of Problems , 1997 .

[53]  P. Meyer.  Probability and potentials , 1966 .

[54]  Bert Fristedt,et al.  A modern approach to probability theory , 1996 .

[55]  Dacunha Castelle Didier,et al.  Probabilités et statistiques. Tome 2 : Problèmes à temps mobile. , 1984 .

[56]  Sheldon M. Ross,et al.  Stochastic Processes , 2018, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[57]  D. Stroock,et al.  Probability Theory: An Analytic View , 1995, The Mathematical Gazette.

[58]  A. Rényi,et al.  Calcul des probabilités , 1966 .

[59]  V. Zolotarev,et al.  Chance and Stability, Stable Distributions and Their Applications , 1999 .

[60]  P. Billingsley,et al.  Probability and Measure , 1980 .

[61]  D. Freedman.  Brownian motion and diffusion , 1971 .

[62]  David Williams,et al.  Probability with Martingales , 1991, Cambridge mathematical textbooks.

[63]  P. Billingsley,et al.  Ergodic theory and information , 1966 .

[64]  D. Stroock.  Markov processes from K. Itô's perspective , 2003 .

[65]  L. Rogers,et al.  Diffusions, Markov Processes and Martingales, Vol. 1, Foundations. , 1996 .

[66]  Michel Loève,et al.  Probability Theory I , 1977 .