Titlebook: Invariant Markov Processes Under Lie Group Actions; Ming Liao Book 2018 Springer International Publishing AG, part of Springer Nature 2018

課程

,Lévy Processes in Compact Lie Groups,The same results are proved in §4.4 for bi-invariant Lévy processes. In this case, the Fourier expansion is given in terms of irreducible characters, a more manageable form of Fourier series. Some examples are computed explicitly in the last section.

不滿分子

Decomposition of Markov Processes,ore detailed study of invariant diffusion processes. As a simple application, in §9.5, we study a diffusion process in a Euclidean space that is invariant under the translations in a subspace. In §9.6, we consider a simple example with jumps.

GREG

皺痕

Invariant Markov Processes Under Lie Group Actions

小木槌

Increment

鎮(zhèn)壓

stics and Lie groups are provided in a series of appendices, making the book accessible to those who may be non-specialists in either of these areas..Invariant Markov Processes Under Lie Group Actions. will be 978-3-030-06406-8978-3-319-92324-6

占卜者

,Spherical Transform and Lévy-Khinchin Formula,niform distribution is obtained in the compact case. The results will be stated in terms of convolution semigroups, and established under a nondegenerate diffusion part or an asymptotic condition on the Lévy measure.

侵略主義

,Inhomogeneous Lévy Processes in Homogeneous Spaces,representation takes an especially simple form in this case. The main results on .∕. may be proved in large part by essentially repeating the proofs on ., with a proper interpretation of group operations on .∕.. More details will be provided in §8.4. Some additional properties are considered in §8.3.

Commodious

lving the interaction of several mathematical areas, such asThe purpose of this monograph is to provide a theory of Markov processes that are invariant under the actions of Lie groups, focusing on ways to represent such processes in the spirit of the classical Lévy-Khinchin representation. It interw