A martingale is a mathematical model of a fair game, or of some other process that is incrementally random noise. The term, which also denotes part of a horse’s harness or a ship’s rigging, refers in addition to a gambling system in which every losing bet is doubled; it was introduced into probability theory by J.L. Doob. Among stochastic processes, martingales have particular constancy properties with respect to conditioning. The time parameter may be either discrete or continuous, but since the latter is more important in economic applications, we concentrate on it.
- Hall, P., and C.C. Heyde. 1980. Martingale limit theory and its applications. New York: Academic Press.Google Scholar
- Karr, A.F. 1986. Point processes and their statistical inference. New York: Marcel Dekker.Google Scholar
- Lipster, R.S., and A.N. Shiryayev. 1978. Statistics of random processes, I and II. Berlin: Springer-Verlag.Google Scholar
- Metivier, M., and J. Pellaumail. 1980. Stochastic integration. New York: Academic Press.Google Scholar