A TCHEBYCHEFF-LIKE INEQUALITY FOR STOCHASTIC PROCESSES.

(X1 + .. . + Xn) 2> + (Aul + ...+ Ang) + a!(V1 + ...+ Vn) (1) is less than 1/(1 + aO3). This bound is sharp. Two lemmas, neither of which are difficult to verify, are used in the proof. The first of these is an application of a familiar fact about semimartingales and optional stopping; see Theorem 3.2, p. 302, of reference 1. LEMMA 1. If Q is bounded from above, t is a stop rule, u < Q, and fo,fi,... is a stochastic process satisfying