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1.
The relation between the upper and lower asymptotic estimates of the density and the fractal dimensions on the sphere of the spectral measure for a multivariate stable distribution is discussed. In particular, the problem and the conjecture on the asymptotic estimates of multivariate stable densities in the work of Pruitt and Taylor in 1969 are solved. The proper asymptotic orders of the stable densities in the case where the spectral measure is absolutely continuous on the sphere, or discrete with the support being a finite set, or a mixture of such cases are obtained. Those results are applied to the moment of the last exit time from a ball and the Spitzer type limit theorem involving capacity for a multi-dimensional transient stable process.

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2.
Periodicity of bounded solutions for convolution equations on a separable abelian metric group is established, and related Liouville type theorems are obtained. A non-constant Borel and bounded harmonic function is constructed for an arbitrary convolution semigroup on any infinite-dimensional separable Hilbert space, generalizing a classical result by Goodman (1973).

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3.
We consider harmonic functions with respect to the operator


Under suitable conditions on we establish a Harnack inequality for functions that are nonnegative and harmonic in a domain. The operator is allowed to be anisotropic and of variable order.

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4.
A probability measure on is called weakly unimodal if there exists a constant such that for all 0$">,

(0.1)

Here, denotes the -ball centered at with radius 0$">.

In this note, we derive a sufficient condition for weak unimodality of a measure on the Borel subsets of . In particular, we use this to prove that every symmetric infinitely divisible distribution is weakly unimodal. This result is then applied to improve some recent results of the authors on capacities and level sets of additive Lévy processes.

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5.
This paper extends the model and analysis of Lin,Tan and Yang(2009).We assume that the financial market follows a regime-switching jump-diffusion model and the mortality satisfies Lvy process.We price the point to point and annual reset EIAs by Esscher transform method under Merton’s assumption and obtain the closed form pricing formulas.Under two cases:with mortality risk and without mortality risk,the effects of the model parameters on the EIAs pricing are illustrated through numerical experiments.  相似文献
6.
本文研究了由一维L′evy过程驱动的倒向随机微分方程(BSDE)的反比较定理。利用一般g -期望下BSDE的反比较定理的证明方法,推导出了一般f -期望下BSDE的反比较定理,并给出了一般f -期望下Jensen不等式成立的充分必要条件。  相似文献
7.
By constructing proper coupling operators for the integro-differential type Markov generator,we establish the existence of a successful coupling for a class of stochastic differential equations driven by L’evy processes.Our result implies a new Liouville theorem for space-time bounded harmonic functions with respect to the underlying Markov semigroups,and it is sharp for Ornstein-Uhlenbeck processes driven by α-stable L’evy processes.  相似文献
8.
本文将经典风险模型的盈余过程推广为一谱正L\'evy过程与一从属L\'evy过程的差,利用L\'evy过程的性质和鞅方法, 得到破产概率的一些结果.对一类谱负的L\'evy过程研究了它的首达时的性质并得出了生存概率的Pollaczek-Khinchin公式.  相似文献
9.
李标  徐静  张波 《数学杂志》2011,(4):599-605
本文研究了平凡可积随机变量的一类非线性期望f-期望.利用陈增敬推广g-期望的方法,扩张了f-期望的定义空间.  相似文献
10.
A novel option pricing method based on Fourier-cosine series expansion was proposed by Fang and Oosterlee. Developing their idea, three new option pricing methods based on Fourier, Fourier-cosine and Fourier-sine series expansions are presented in this paper, which are more efficient when the option prices are calculated with many strike prices. A series of numerical experiments under different exp-L~vy models are also given to compare these new methods with the Fang and Oosterlee's method and other methods.  相似文献
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