Differentiability of spectral functions for nearly stable processes and large deviations

Yoshihiro Tawara; Kaneharu Tsuchida

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Differentiability of spectral functions for nearly stable processes and large deviations

机译：光谱函数的可微性，用于接近稳定的过程和较大的偏差

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摘要

We consider the differentiability of a spectral function generated by a Lévy process M with characteristic exponent |ξ|~αl(|ξ|~2), where l(x) is a slowly varying function at ∞. As an application, we obtain the large deviation principle for positive continuous additive functionals of M. Finally, we show that the exponent l(x) = (log(1 + x))~(β/2) (0< β< 2 - α) is an example for which our theorem is applicable.

机译：我们考虑由Lévy过程M生成的具有特征指数|ξ|〜αl（|ξ|〜2）的谱函数的可微性，其中l（x）是在∞处的缓慢变化的函数。作为应用，我们获得了M的正连续加性泛函的大偏差原理。最后，我们证明了指数l（x）=（log（1 + x））〜（β/ 2）（0 <β<2 -α）是适用我们定理的一个例子。

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《Infinite dimensional analysis, quantum probability, and related topics》 |2014年第3期|共15页
作者
Yoshihiro Tawara; Kaneharu Tsuchida;
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正文语种 eng
中图分类物理学;
关键词
Large deviation; symmetric Markov process; additive functional; subordinate Brownian motion; nearly stable process;

机译：大偏差;对称马尔可夫过程;加法函数;从属布朗运动;近稳定过程;

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专利

1. Differentiability of spectral functions for nearly stable processes and large deviations [J] . Yoshihiro Tawara, Kaneharu Tsuchida Infinite dimensional analysis, quantum probability, and related topics . 2014,第3期

机译：光谱函数的可微性，用于接近稳定的过程和较大的偏差
2. Differentiability of spectral functions for relativistic alpha-stable processes with application to large deviations [J] . Tsuchida K Potential analysis: An international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis . 2008,第1期

机译：相对论α稳定过程光谱函数的微分性并应用于大偏差
3. Differentiability of spectral functions for symmetric alpha-stable processes [J] . Takeda M, Tsuchida K Transactions of the American Mathematical Society . 2007,第8期

机译：对称α稳定过程的光谱函数的可微性
4. On finite-time stable tracking differentiator without Lipschitz continuity of Lyapunov function [C] . Guo Bao-Zhu, Zhao Zhi-Liang 2011 30th Chinese Control Conference . 2011

机译：Lyapunov函数没有Lipschitz连续性的有限时间稳定跟踪微分
5. A functional LIL for d-dimensional alpha-stable processes: Invariance for Levy- and other weakly convergent processes. [D] . Rushton, Joshua D. 2005

机译：用于d维alpha稳定过程的功能性LIL：对于Levy和其他弱收敛过程的不变性。
6. Bayesian Smoothing with Gaussian Processes Using Fourier Basis Functions in the spectralGP Package [O] . Christopher J. Paciorek -1

机译：使用光谱GP软件包中的傅立叶基函数进行高斯过程的贝叶斯平滑
7. Differentiability of spectral functions for symmetric $lpha$-stable processes [O] . Masayoshi Takeda, Kaneharu Tsuchida 2007

机译：对称$ Alpha $ -stable进程的光谱函数的可分性

Differentiability of spectral functions for nearly stable processes and large deviations

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