科研之友
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摘要
Let X = (Xt)(t >= 0) be a nonnegative semimartingale and H = (H(t))(t >= 0) be a predictable process taking values in [-1,1]. Let Y denote the stochastic integral of H with respect to X. We show that (i) If X is a supermartingale, then parallel to sup(t >= 0)Y(t)parallel to(1) <= 3 parallel to sup(t >= 0)X(t)parallel to(1) and the constant 3 is the best possible. (ii) If X is a submartingale satisfying parallel to X parallel to(infinity) <= 1, then parallel to sup(t >= 0)Y(t)parallel to(p) <= 2 Gamma(p+1)(1/p), 1 <= p <= infinity. The constant 2 Gamma(p+1)(1/p) is the best possible.
- 出版日期2011-7
