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8. Brownian motion
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8.3
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8.6
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9.The strong Markov property of Brownian motion
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9.2
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10.Martingales
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11.The Donsker invariance principe
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12.An outlook to stochastic integration
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13.Exercises
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1.P.Billingsley: Probability and Measure, Wiley and sons, New-York, 1979
2.L.Breiman: Probability, Addison-Wesley, Reading, 1968
3.W. B. Davenport, Jr. and W. L. Root,An Introduction to the Theory of Random Signals and Noise.
New York, NY, USA: McGraw-Hill Inc., 1958.4.W. B. Davenport, Jr., Probability and Random Processes: An Introduction for Applied
Scientists and Engineers. New York, NY, USA: McGraw-Hill Inc., 1970.
5.J. L. Doob, Stochastic Processes. New York, NY, USA: John Wiley & Sons Inc.,1958.
7.W. Feller An introduction to probability theory and its application Tome I&II. Wiley(1966)
8. J. E. Freund,Mathematical Statistics. Englewood Cliffs, NJ, USA: Prentice-Hall, Inc.,
16th printing, 1962.
9.J. E. Freund and G. A. Simon, Modern Elementary Statistics. Englewood Cliffs, NJ,
USA: Prentice-Hall, Inc., 8th ed., 1992.
10.W. A. Gardner, Introduction to Random Processes with Applications to Signals andSystems. London, UK: Collier Macmillan Publishers, 1986.
11.Peter Galko, ELG 5119/92.519 Stochastic Processes Course Notes, Faculty of
Engineering, University of Ottawa, Ottawa, ON, Canada, Fall 1987.
12.W. A. Gardner, Introduction to Random Processes with Applications to Signals and
Systems. New York, NY, USA: McGraw-Hill Publishing Company, 2nd ed., 1990.
13. B. V. Gnedenko, Theory of Probability. New York, NY, USA: Chelsea Publishing
Co., 1962. Library of Congress Card No. 61-13496.
14.R. M. Gray and L. D. Davisson,Random Processes: A Mathematical Approach for
Engineers. Englewood Cliffs, NJ, USA: Prentice-Hall, Inc., 1986.
15.H. P. Hsu,Schaum's outline of theory and problems of probability, random variables,
and random processes. New York, NY, USA: McGraw-Hill Inc., 1997.
16.A. N. Kolmogorov,Foundations of the Theory of Probability. New York, NY, USA:
Chelsea Publishing Co., english translation of 1933 german edition, 2nd english ed.,1956.
17.Alberto Leon-Garcia,Probability and Random Processes for Electrical Engineering
Reading, MA, USA: Addison Wesley Publishing Co. Inc., 2nd ed., 1994. ISBN 0-201-
50037-X.
18.Alberto Leon-Garcia, Student Solutions Manual: Probability and Random Processes
for Electrical Engineering. Reading, MA, USA: Addison-Wesley Publishing Co. Inc.,
2nd ed., 1994. ISBN 0-201-55738-X.
19.M. Love,Probability Theory. Princeton, NJ, USA: D. Van Nostrand Co., Inc., 2nded., 1960.
20.M. Love, Probability Theory, vol. I. New York, NY, USA: Springer, 4th ed., 1977.
21.M. Love, Probability Theory, vol. II. New York, NY, USA: Springer, 4th ed., 1978.
22.I. Miller and J. E. Freund,Probability and Statistics for Engineers. Englewood Cliffs,
NJ, USA: Prentice-Hall, Inc., 2nd ed., 1977.
Bibliography:
A.BENHARI 155
6.R.Durrett.Probability:Theory and examples.Duxbury press, 1996
7/29/2019 Lecture Notes on Probability Theory
157/157
26.Athanasios Papoulis, Probability, Random Variables, and Stochastic Processes.
NewYork, NY, USA: McGraw-Hill Inc., 3rd ed., 1991. ISBN 0-07-048477-5.
27.Yu Rozanov,Probability Theory, Random Processes, and Mathematical Statistics,
Kluwer Academic Publishers, 199528.Sheldon Ross.A First Course in Probability. Englewoods CLiffs, NJ, USA: Prentice-Hall, Inc., 1994.
29.A.N.Shiriyaev: Probability, Springer-Verlag, New-York, 1984
30.Gihman,I.I.;Skorohod A.V. The theory of stochastic processes . Springer-verlag, Berlin/heidelberg/
New york 1974.
31. H. L. Van Trees, Detection, Estimation and Modulation Theory, Part I: Detection,Estimation,
and Linear Modulation Theory.New York, USA Wiley&Sons INc., 1968.
32.Todorovic P. , An introduction to stochastic processes and their application. Springer- Verlag,
Springer Series in statistics 1992
33. Y. Viniotis, Probability and Random Processes for Electrical Engineering. New York,NY, USA:
McGraw-Hill Inc., 1998.34.N. Wiener,Nonlinear Problems in Random Theory. Cambridge, MA, USA: The M.I.T.Press, 1966.
35.D.Williams: Probability with Martingales, Cambridge Math.Textbooks, Cambridge,1991
36.Roy D. Yates and David J. Goodman, Probability and Stochastic Processes, John Wiley and Sons,
Second Edition, 2005
23.J.R.Norris: Markov chains, Cambridge University Press, 1997
24 M O'Flynn Probabilities Random Variables and Stochastic Processes New York NY USA:
