文献类型：期刊文献

英文题名：A LAW OF THE ITERATED LOGARITHM FOR STOCHASTIC INTEGRALS

作者：WANG, JG

年份：1993

卷号：47

期号：2

起止页码：215

外文期刊名：STOCHASTIC PROCESSES AND THEIR APPLICATIONS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:A1993LY08200004)】；

语种：英文

摘要：By using the Ito calculus, a law of the iterated logarithm (LIL) is established for stochastic integrals with respect to locally square integrable martingales. Let M = (M(t), t greater-than-or-equal-to 0) be a d-dimensional locally square integrable martingale, B = (B(t)) be a d-dimensional predictable process and X = B(T). M. If lim(t-->infinity)[X]t = infinity a.s., \B(t)\2 = o([X]t(beta) beta < 1 and there exists a majorant measure for the Levy system of M, then [GRAPHICS] As an application of this LIL, a LIL for the quadratic form of i.i.d. random variables is given. In particular, let {xi(n), n greater-than-or-equal-to 1} be a sequence of i.i.d. random variables with Exi(n) = 0, Exi(n)2 = sigma2 > 0 and Exi(n)4 = mu4 < infinity. If [GRAPHICS] Then for all lambda is-an-element-of (0, pi], [GRAPHICS] AMS 1980 Subject Classification (1985 Revision): 60F15, 60G44, 60H05, 62M15.