000			01969nam a2200205 4500
005			20251203115137.0
008			251029b |||||||| |||| 00| 0 eng d
020			_a97833199823239
041			_aeng
082			_a519.2 _bLiaI
100			_aLiao, Ming
245			_aInvariant markov Process under lie Group Actions/ _cMing Liao
260			_aNewyork: _bSpringer, _c©2018
300			_ax, 361p.
520			_aThe 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 Levy-Khinchin representation. It interweaves probability theory, topology, and global analysis on manifolds to present the most recent results in a developing area of stochastic analysis. The author's discussion is structured with three different levels of generality:- A Markov process in a Lie group G that is invariant under the left (or right) translations- A Markov process xt in a manifold X that is invariant under the transitive action of a Lie group G on X- A Markov process xt invariant under the non-transitive action of a Lie group GA large portion of the text is devoted to the representation of inhomogeneous Levy processes in Lie groups and homogeneous spaces by a time dependent triple through a martingale property. Preliminary definitions and results in both stochastics 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 of interest to researchers in stochastic analysis and probability theory, and will also appeal to experts in Lie groups, differential geometry, and related topics interested in applications of their own subjects.
650			_aNatural sciences & mathematics
650			_aProbabilities
650			_aProbabilities and applied mathematics
942			_cBK
999			_c7588 _d7588