Matsumoto和Yor过程与infinite dimensional双曲空间
The Matsumoto and Yor process and infinite dimensional hyperbolic space
摘要：
Matsumoto\，--Yor过程是$\int\_0^t \exp(2B\_s-B\_t)\, ds$，其中$(B\_t)$是布朗运动。证明了当$q$趋于无穷大时，它是$q$维双曲空间上布朗运动径向部分在谱底的极限.描述了非紧对称空间上的无穷级数和正则树上的类似过程。
英文摘要：
The Matsumoto\,--Yor process is $\int\_0^t \exp(2B\_s-B\_t)\, ds$, where $(B\_t)$ is a Brownian motion. It is shown that it is the limit of the radial part of the Brownian motion at the bottom of the spectrum on the hyperbolic space of dimension $q$, when $q$ tends to infinity. Analogous processes on infinite series of non compact symmetric spaces and on regular trees are described.
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