Vol. 61, No. 2, 1975

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Properties of martingale-like sequences

R. James Tomkins

Vol. 61 (1975), No. 2, 521–525

The purpose of this paper is to define a new type of stochastic sequence and to explore its properties. These new sequences of random variables, called eventual martingales, generalize the concept of a martingale.

Several known results concerning the almost sure limiting behavior of martingales are shown to remain valid for eventual martingales. In addition, eventual martingales are compared with three other martingale-like sequences.

Mathematical Subject Classification
Primary: 60G45, 60G45
Received: 23 January 1975
Published: 1 December 1975
R. James Tomkins