Abstract

Stochastic processes that take values in the group of orthogonal transformations of a finite-dimensional Euclidean space and are noncommutative analogues of processes with independent increments are considered. Such processes are defined as limits of noncommutative analogues of random walks in the group of orthogonal transformations. These random walks are compositions of independent random orthogonal transformations of Euclidean space. In particular, noncommutative analogues of diffusion processes with values in the group of orthogonal transformations are defined in this manner. Kolmogorov backward equations are derived for these processes.

中文翻译：

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正交矩阵群上的随机过程和描述它们的演化方程

摘要

考虑了随机过程，该过程采用有限维欧氏空间正交变换组中的值，并且是具有独立增量的过程的非交换类似物。这样的过程被定义为正交变换组中随机游走的非交换类似物的极限。这些随机游走是欧几里德空间的独立随机正交变换的组成。特别地，以这种方式定义了具有正交变换组中的值的扩散过程的非可交换类似物。针对这些过程推导了Kolmogorov向后方程。