When Can Martingales Avoid Ruin?
نویسندگان
چکیده
We provide conditions that guarantee for a discrete time martingale Mn, either limn→∞Mn exists, or both lim supn→∞Mn = ∞ and lim infn→∞Mn = −∞, a.s. on sample paths. A sufficient condition on the martingale is a uniform control on the ratio of the L2 and L1 norms of the increments. Near-symmetry of the increments provides an alternative condition. We also discuss a counterexample when these conditions are violated.
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تاریخ انتشار 2004