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作者：Foss, Serguei; Korshunov, Dmitry
作者单位：Heriot Watt University
摘要：Suppose F is a distribution on the half-line [0, infinity). We study the limits of the ratios of tails F * F(x) vertical bar F(x) as x -> infinity. We also discuss the classes of distributions s, s(y) and s*.
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作者：Hult, Henrik; Lindskog, Filip
作者单位：Brown University; Royal Institute of Technology
摘要：We study the extremal behavior of a stochastic integral driven by a multivariate Levy process that is regularly varying with index alpha > 0. For predictable integrands with a finite (alpha + delta)-moment, for some delta > 0, we show that the extremal behavior of the stochastic integral is due to one big jump of the driving Levy process and we determine its limit measure associated with regular variation on the space of cadlag functions.
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作者：Fang, Shizan; Imkeller, Peter; Zhang, Tusheng
作者单位：Universite Bourgogne Europe; Humboldt University of Berlin; University of Manchester
摘要：We consider stochastic differential equations driven by Wiener processes. The vector fields are supposed to satisfy only local Lipschitz conditions. The Lipschitz constants of the drift vector field, valid on balls of radius R, are supposed to grow not faster than log R, while those of the diffusion vector fields are supposed to grow not faster than root log R. We regularize the stochastic differential equations by associating with them approximating ordinary differential equations obtained by...
