Abstract
We will treat what many would regard as the most important type of random sequence, for it is both intrinsically natural and also a tool for treating other topics in probability. Martingales are particularly important in the study of Markov sequences and Markov processes, as will be seen later in this book.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Billingsley, Patrick, Convergence of Probability Measures, John Wiley & Sons, New York, 1968.
Dellacherie, Claude and Meyer, Paul-André, Probabilities and Potential B (translated from French, orig. 1980), North-Holland, Amsterdam, 1982.
Durrett, Richard, Brownian Motion and Martingales in Analysis, Wadsworth Advanced Books & Software, Belmont, California, 1984.
Durrett, Richard, Stochastic Calculus: A Practical Introduction, CRC Press, Boca Raton, Florida, 1996.
Einstein, Albert, Investigations on the Theory of the Brownian Movement, Dover, New York, 1956.
Freedman, David, Brownian Motion and Diffusion, Holden-Day, San Francisco, 1971.
Friedman, Avner, Stochastic Differential Equations and Applications, Vol. 1, Academic Press, New York, 1975.
Friedman, Avner, Stochastic Differential Equations and Applications, Vol. 2., Academic Press, New York, 1976.
Gard, Thomas C, Introduction to Stochastic Differential Equations, Marcel Dekker, New York, 1988.
Gihman, I. I. and Skorohod, A. V., Controlled Stochastic Processes, Springer-Verlag, New York, 1979.
He, Shengwu and Wang, Jiagang and Yan, Jiaan, Semimartingale Theory and Stochastic Calculus, CRC Press, Boca Raton, Florida, 1992.
Hida, Takeyuki, Brownian Motion, Springer-Verlag, New York, 1980.
Ikeda, Nobuyuki and Watanabe, Shinzo, Stochastic Differential Equations and Diffusion Processes, Second Edition, Kodansha, Tokyo, 1989.
ItĂ´, Kiyosi, Foundations of Stochastic Differential Equations in Infinite Dimensional Spaces, Society for Industrial and Applied Mathematics, Philadelphia, 1984.
ItĂ´, K. and McKean Jr., H. P., Diffusion Processes and Their Sample Paths, Springer-Verlag, Berlin, 1974.
Krylov, N. V., Introduction to the Theory of Diffusion Processes, American Mathematical Society, Providence, Rhode Island, 1995.
Ledoux, Michel and Talagrand, Michel, Probability in Banach Spaces, Springer-Verlag, Berlin, 1991.
Lukacs, Eugene, Stochastic Convergence, Second Edition, Academic Press, New York, 1975.
McKean Jr., H. P., Stochastic Integrals, Academic Press, New York, 1969.
Metivier, Michel and Pellaumail, J., Stochastic Integration, Academic Press, New York, 1980.
Metivier, Michel, Semimartingales, a Course on Stochastic Processes, Walter de Gruyter, Berlin, 1982.
Meyer, Paul A., Probability and Potentials, Blaisdell, Waltham, Massachusetts, 1966.
Nualart, David, The Malliavin Calculus and Related Topics, Springer-Verlag, New York, 1995.
Parthasarathy, K. R., Probability Measures on Metric Spaces, Academic Press, New York, 1967.
Portenko, N. I., Generalized Diffusion Processes (translation from Russian, orig. 1982), American Mathematical Society, Providence, Rhode Island, 1990.
Revuz, Daniel and Yor, Marc, Continuous Martingales and Brownian Motion, Second Edition, Springer-Verlag, Berlin, 1994.
Rogers, L. C. G. and Williams, David, Diffusions, Markov Processes, and Martingales, Vol 2: Ito Calculus, John Wiley & Sons, Chichester, 1987.
Skorohod, A. V., Asymptotic Methods in the Theory of Stochastic Differential Equations (translated from Russian, orig. 1987), American Mathematical Society, Providence, Rhode Island, 1989.
Stroock, D. W. and Varadhan, S.R. S., Multidimensional Diffusion Processes, Springer-Verlag, Berlin, 1979.
Yeh, J., Stochastic Processes and the Wiener Integral, Marcel Dekker, New York, 1973.
Yor, Marc, Some Aspects of Brownian Motion: Part I: Some Special Functionals, Birkhäuser Verlag, Basel, Switzerland, 1992.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media New York
About this chapter
Cite this chapter
Fristedt, B., Gray, L. (1997). Martingales. In: A Modern Approach to Probability Theory. Probability and its Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-2837-5_24
Download citation
DOI: https://doi.org/10.1007/978-1-4899-2837-5_24
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4899-2839-9
Online ISBN: 978-1-4899-2837-5
eBook Packages: Springer Book Archive