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A law of the iterated logarithm for stochastic integrals

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  • Wang, Jia-gang

Abstract

By using the Itô calculus, a law of the iterated logarithm (LIL) is established for stochastic integrals with respect to locally square integrable martingales. Let M = (Mt, t [greater-or-equal, slanted] 0) be a d-dimensional locally square integrable martingale, B = (Bt) be a d-dimensional predictable process and X = BT · M. If limt-->[infinity] t = [infinity] a.s., Bt2 = o( [beta]t), [beta] 0 and E[xi]4n = [mu]4

Suggested Citation

  • Wang, Jia-gang, 1993. "A law of the iterated logarithm for stochastic integrals," Stochastic Processes and their Applications, Elsevier, vol. 47(2), pages 215-228, September.
    • Handle: RePEc:eee:spapps:v:47:y:1993:i:2:p:215-228
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    Cited by:

    1. Паламарчук Е.С., 2013. "Оценка Риска В Линейных Экономических Системах При Отрицательных Временных Предпочтениях," Журнал Экономика и математические методы (ЭММ), Центральный Экономико-Математический Институт (ЦЭМИ), vol. 49(3), pages 99-116, июль.
    2. Yuichi Shiozawa & Jian Wang, 2021. "Martingale Nature and Laws of the Iterated Logarithm for Markov Processes of Pure-Jump Type," Journal of Theoretical Probability, Springer, vol. 34(4), pages 2005-2032, December.

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