多分数Lvy过程的混沌展开（英文）

本文研究了多分数Lvy过程的混沌展开.利用白噪声分析方法,给出了多分数Lvy过程的混沌展开.进一步地,给出其Lvy-Hermite变换和Malliavin导数.     

带扰动Lévy风险过程的G-S函数

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.     

基于构造的Brown单Lévy连续模

该文利用Schauder函数建立了Brown单的级数表示．基于该表示，作者得到它的Lévy连续模的简化证明．     

Lévy过程驱动的BSDE的反比较定理与Jensen不等式

本文研究了由一维Lévy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.     

Gel’fand三元组上由同一Lévy过程定义的不同分数Lévy过程之间的积分变换公式(英文)

本文利用Riemann-Liouville分数积分算子的半群性质以及分数Lévy过程的Wie-ner积分,给出由同一平方可积Lévy过程定义的不同分数Lévy过程之间的积分变换公式.     

Gel’fand三元组上多分数Lévy过程(英文)

本文研究了Gel’fand三元组上多分数Lévy过程.通过将分数Lévy过程的参数替换为依赖于时间t的函数,从而定义了Gel’fand三元组上的多分数Lévy过程以及其一维边际分布和协方差函数.     

关于Lévy过程一个公开问题的部分回答

令{X_t,t∈R~+}是一Lévy过程,令γ_0=sup{α≥0:lim inf a~(-α)ET(a,1)<∞},这里T(a,1)=integral from 0 to 1 I{|X_t|≤a}dt.Taylor证明X_t的像集的填充维数等于γ0.由Pruitt和Taylor提出的一个公开问题是:等式γ_0=inf{α≥0:a~(-α)T(a,1)→∞a.s.,当a→0}是否成立?文中证明了:当{X_t,t∈R~+}是从属过程时,上述等式成立.     

基于指数Lévy过程的随机债券利率欧式外币期权定价

本文考虑国内外债券利率均为随机条件下的欧式外币期权定价.外币价格,国内外利率均用指数Lévy过程描述.并将本文的模型与经典的Black-Scholes模型进行了比较.     

非Lipschitz条件下由Lévy过程驱动的倒向随机微分方程解的存在唯一及其稳定性

本文研究了由满足某种矩条件下Lévy过程相应的Teugel鞅及与之独立的布朗运动驱动的倒向随机微分方程,给出了飘逸系数满足非Lipschitz条件下解的存在唯一及稳定性结论.解的存在性是通过Picard迭代法给出的.解的L2收敛性是在飘逸系数弱于L2收敛意义下所得到的.     

两指标Lévy过程的Lévy Markov性

关于两指标过程的Lévy Markov性,[2]证明了:对于广义Brownian Sheet和广义OUP_2,对适当的DR_+,有: 那里充分利用了过程的轨道连续性及正态系的一个性质:独立性等价于不相关性,[2]的这个结果使[1]中结果 (对一般的两指标Markov过程成立)对此特殊过程得到改进,本文的结果是:对于随机连续的独立增量过程(即两指标Lévy过程),对具有分段光滑边界的D∈B_+,有:由于两指标Lévy过程以广义Brownian Sheet,广义OUP_2及Poisson单为特例,故此结果推广了[2]的结果,而方法不同于[2]     

A Smooth Approach to Malliavin Calculus for Lévy Processes

An approach to Malliavin calculus for Lévy processes, discrete in time and smooth in chance, is presented. Each Lévy triple can be satisfied by a Lévy process living on a fixed sample space Ω, which is, in a certain sense, a finite dimensional Euclidean space. The probability measures on Ω characterize the Lévy processes. We compare these measures with the associated Lévy measures, and present several examples. Using chaos expansions for Lévy functionals, even for those having no moments, we can represent all these functionals by polynomials in several variables. There exists an effective method to compute the kernels of the chaos decomposition. Finally, we point out several applications, which are postponed to a succession of papers. Dedicated to Helmut Schwichtenberg.     

Transportation Cost Inequalities for Stochastic Reaction-Diffusion Equations with Lévy Noises and Non-Lipschitz Reaction Terms

For stochastic reaction-diffusion equations with Levy noises and non-Lipschitz reaction terms,we prove that W\H transportation cost inequalities hold for their invariant probability measures and for their process-level laws on the path space with respect to the L1-metrie.The proofs are based on the Galerkin approximations.     

Efficient estimation methods for non-Gaussian regression models in continuous time

Annals of the Institute of Statistical Mathematics - In this paper, we develop an efficient nonparametric estimation theory for continuous time regression models with non-Gaussian Lévy noises...     

White Noise of Poisson Random Measures

We develop a white noise theory for Poisson random measures associated with a pure jump Lévy process. The starting point of this theory is the chaos expansion of Itô. We use this to construct the white noise of a Poisson random measure, which takes values in a certain distribution space. Then we show, how a Skorohod/Itô integral for point processes can be represented by a Bochner integral in terms of white noise of the random measure and a Wick product. Further, based on these concepts we derive a generalized Clark–Haussmann–Ocone theorem with respect to a combination of Gaussian noise and pure jump Lévy noise. We apply this theorem to obtain an explicit formula for partial observation minimal variance portfolios in financial markets, driven by Lévy processes. As an example we compute the closest hedge to a binary option.     

Transition densities of spectrally positive Lévy processes

Lithuanian Mathematical Journal - We deduce the asymptotic behavior of transition densities for a large class of spectrally one-sided Lévy processes of unbounded variation satisfying mild...     

Symmetric stable processes in parabola-shaped regions

We identify the critical exponent of integrability of the first exit time of the rotation invariant stable Lévy process from a parabola-shaped region.

     

Multifractional Markov Processes in Heterogeneous Domains

In this article, we introduce a class of Markov processes whose transition probability densities are defined by multifractional pseudodifferential evolution equations on compact domains with variable local dimension. The infinitesimal generators of these Markov processes are given by the trace of strongly elliptic pseudodifferential operators of variable order on such domains. The results derived provide a pseudomultifractal version of some existing special classes of multifractional Markov processes. In particular, pseudostable processes are defined on domains with variable local dimension in this framework. In the case where the local dimension of the domain and the local Hölder exponents of the transition probability densities are constant, the existing results on fractal versions of Lévy processes are recovered.     

White noise analysis for Lévy processes

We construct a white noise theory for Lévy processes. The starting point of this theory is a chaos expansion for square integrable random variables. We use this approach to Malliavin calculus to prove the following white noise generalization of the Clark-Haussmann-Ocone formula for Lévy processes

     

A combinatorial method for calculating the moments of Lévy area

We present a new way to compute the moments of the Lévy area of a two-dimensional Brownian motion. Our approach uses iterated integrals and combinatorial arguments involving the shuffle product.