共查询到11条相似文献,搜索用时 0 毫秒
1.
B. Buchmann 《Mathematical Methods of Statistics》2009,18(4):281-309
Given observations of a Lévy process, we provide nonparametric estimators of its Lévy tail and study the asymptotic properties
of the corresponding weighted empirical processes. Within a special class of weight functions, we give necessary and sufficient
conditions that ensure strong consistency and asymptotic normality of the weighted empirical processes, provided that complete
information on the jumps is available. To cope with infinite activity processes, we depart from this assumption and analyze
the weighted empirical processes of a sampling scheme where small jumps are neglected. We establish a bootstrap principle
and provide a simulation study for some prominent Lévy processes. 相似文献
2.
In this paper,we study a general Lévy risk process with positive and negative jumps.A renewal equation and an infinite series expression are obtained for the expected discounted penalty function of this risk model.We also examine some asymptotic behaviors for the ruin probability as the initial capital tends to infinity. 相似文献
3.
For the two-dimensional Walsh system, Gat and Weisz proved the a.e. convergence of Fejer means σnf of integrable functions, where the set of indices is inside a positive cone around the identical function, that is, β^-1≤n1/n2 ≤β is provided with some fixed parameter ~ 〉 1. In this paper we generalize the result of Gat and Weisz. We not only generalize this theorem, but give a necessary and sufficient condition for cone-like sets in order to preserve this convergence property. 相似文献
4.
In this paper,we consider the problem of testing for an autocorrelation change in discretely observed Ornstein-Uhlenbeck processes driven by Lévy processes.For a test,we propose a class of test statistics constructed by an iterated cumulative sums of squares of the difference between two adjacent observations.It is shown that each of the test statistics weakly converges to the supremum of the square of a Brownian bridge.The test statistics are evaluated by some empirical results. 相似文献
5.
6.
7.
Consider the optimal dividend problem for an insurance company whose uncontrolled surplus precess evolves as a spectrally negative Levy process. We assume that dividends are paid to the shareholders according to admissible strategies whose dividend rate is bounded by a constant. The objective is to find a dividend policy so as to maximize the expected discounted value of dividends which are paid to the shareholders until the company is ruined. In this paper, we show that a threshold strategy (also called refraction strategy) forms an optimal strategy under the condition that the Levy measure has a completely monotone density. 相似文献
8.
KIM KyeongHun 《中国科学 数学(英文版)》2012,55(11):2233-2246
In this paper we present an L 2-theory for a class of stochastic partial differential equations driven by Lévy processes.The coefficients of the equations are random functions depending on time and space variables,and no smoothness assumption of the coefficients is assumed. 相似文献
9.
通过对带扰动项的Lévy风险过程的研究得到了其罚金折现期望(G-S)函数满足的更新方程,并给出了它的一个无穷级数表达式. 相似文献
10.
In this paper we prove the uniform boundary Harnack principle in general open sets for harmonic functions with respect to a large class of rotationally symmetric purely discontinuous Lvy processes. 相似文献
11.
In this paper, we establish the discrete approximation of continuous-state nonlinear branching processes in Lévy random environments by using tightness and convergence sequence in infinite dimensional product space via stochastic differential equations. Taking α-stable branching as an example, the conditions which are given to discretize continuous-state nonlinear branching processes in Lévy random environments are verified. © 2022 Chinese Academy of Sciences. All rights reserved. 相似文献