Sample functions of certain differential processes on symmetric spaces
Sample functions of certain differential processes on symmetric spaces
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对称空间上某些微分过程的样本函数
DOI：
10.2140/pjm.1965.15.477
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发表时间：
1965
影响因子：
0.6
通讯作者：
R. Gangolli
中科院分区：
文献类型：
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作者：
R. Gangolli
在最近的一篇文章中，我们证明了一个刻画对称空间上各向同性ίc无穷可分概率测度的抽象傅立叶-斯蒂尔杰斯变换的公式。该公式是实线上无限可分概率测度的傅里叶-斯蒂尔杰斯变换的经典L公式的完全类比。现在，就像直线的情况一样，对称空间上的各向同性、无限可分的概率测度以一种自然的方式产生这样的测度的连续的单参数卷积半群，从而产生具有平稳独立“增量”的随机过程。本文的目的是构造这样一个过程的样本函数。我们将展示这样一个过程的样本函数，即交织着有限多个各向同性泊松跳跃的连续布朗轨迹序列的概率极限为1(一致地在参数集的紧致子集上)。
In a recent paper, we have proved a formula characterizing the abstract Fourier-Stieltjes transform of an isotropίc infinitely divisible probability measures on a symmetric space. The formula is the full analogue of the classical L§vy-Khinchine formula for the Fourier-Stieltjes transform of infinitely divisible probability measures on the real line. Now, just as in the case of the line, an isotropic, infinitely divisible probability measure on a symmetric space gives rise in a natural way to a continuous one parameter convolution semigroup of such measures and thence to a stochastic process with stationary independent " increments ". It is the purpose of this paper to construct the sample functions of such a process. We shall exhibit the sample functions of such a process as limits with probability one (uniformly on compact subsets of the parameter set) of sequences of continuous Brownian trajectories interlaced with finitely many isotropic Poissonian jumps.
DOI：
10.1002/9781118231296.ch8
发表时间：
2018-11
期刊：
Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics
影响因子：
--
作者：
Dr. Gergely Záruba
通讯作者：
Dr. Gergely Záruba