Universality of the asymptotics of the one-sided exit problem for integrated processes
Universality of the asymptotics of the one-sided exit problem for integrated processes
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DOI：
10.1214/11-aihp427
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发表时间：
2010-08
期刊：
影响因子：
--
通讯作者：
F. Aurzada;S. Dereich
中科院分区：
文献类型：
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作者：
F. Aurzada;S. Dereich
我们考虑（分数）集成随机游走和 L'evy 过程的单边退出问题。我们证明，不退出概率的下降率（即所谓的生存指数）在此类过程中是普遍存在的。特别是，生存指数可以从（分数）积分布朗运动推断出来。特别是，这将西奈关于积分简单随机游走的生存指数的结果扩展到具有某些有限指数矩的一般随机游走。此外，我们证明了分数积分过程的生存指数的存在性和单调性。我们证明该指数与随机多项式研究中出现的常数有关。
We consider the one-sided exit problem for (fractionally) integrated random walks and L\'evy processes. We prove that the rate of decrease of the non-exit probability -- the so-called survival exponent -- is universal in this class of processes. In particular, the survival exponent can be inferred from the (fractionally) integrated Brownian motion. This, in particular, extends Sinai's result on the survival exponent for the integrated simple random walk to general random walks with some finite exponential moment. Further, we prove existence and monotonicity of the survival exponent of fractionally integrated processes. We show that this exponent is related to a constant appearing in the study of random polynomials.