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Sharp inequality for bounded submartingales and their differential subordinates
2008
Electronic Communications in Probability
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For any fixed α ∈ [0, 1] and λ > 0 we determine the optimal function V α,λ satisfying for any submartingale f = (fn) bounded in absolute value by 1 and any process g = (gn) which is real-valued, adapted, integrable and satisfying |dgn| ≤ |dfn| and |E(dgn|F n−1 )| ≤ αE(dfn|F n−1 ), n = 1, 2 . . . , with probability 1. As a corollary, a sharp exponential inequality for the distribution function of maxn |gn| is established. 1991 Mathematics Subject Classification. Primary: 60G42. Secondary: 60G46.
doi:10.1214/ecp.v13-1433
fatcat:blqu7a2o7jdn5pjwytg7hfxi5m