Stochastic Analysis on Lie Groups

1998 ◽  
pp. 129-158 ◽  
Author(s):  
A. S. Üstünel
Keyword(s):  
Lie Groups ◽  
Stochastic Analysis

scholarly journals VARIETIES OF SIGNATURE TENSORS

2019 ◽  
Vol 7 ◽  
Author(s):  
CARLOS AMÉNDOLA ◽  
PETER FRIZ ◽  
BERND STURMFELS
Keyword(s):  
Brownian Motion ◽  
Algebraic Geometry ◽  
Lie Groups ◽  
Stochastic Analysis ◽  
Piecewise Linear ◽  
Nilpotent Lie Groups ◽  
Rough Paths ◽  
Iterated Integrals ◽  
Parametric Curve

The signature of a parametric curve is a sequence of tensors whose entries are iterated integrals. This construction is central to the theory of rough paths in stochastic analysis. It is examined here through the lens of algebraic geometry. We introduce varieties of signature tensors for both deterministic paths and random paths. For the former, we focus on piecewise linear paths, on polynomial paths, and on varieties derived from free nilpotent Lie groups. For the latter, we focus on Brownian motion and its mixtures.

scholarly journals Random transformations and invariance of semimartingales on Lie groups

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sergio Albeverio ◽  
Francesco C. De Vecchi ◽  
Paola Morando ◽  
Stefania Ugolini
Keyword(s):  
Brownian Motion ◽  
Lie Groups ◽  
Stochastic Analysis ◽  
Invariance Properties ◽  
Explicit Condition ◽  
Stochastic Characteristics ◽  
Necessary And Sufficient

Abstract Invariance properties of semimartingales on Lie groups under a family of random transformations are defined and investigated, generalizing the random rotations of the Brownian motion. A necessary and sufficient explicit condition characterizing semimartingales with this kind of invariance is given in terms of their stochastic characteristics. Non-trivial examples of symmetric semimartingales are provided and applications of this concept to stochastic analysis are discussed.

Lie Groups, Lie Algebras, Cohomology and some Applications in Physics

1995 ◽  
Author(s):  
Josi A. de Azcárraga ◽  
Josi M. Izquierdo
Keyword(s):  
Lie Groups ◽  
Lie Algebras

Wavelet-based model for stochastic analysis of beam structures

AIAA Journal ◽  
1998 ◽  
Vol 36 ◽  
pp. 465-470 ◽  
Author(s):  
Hong Mei ◽  
Om P. Agrawal ◽  
Shantaram S. Pai
Keyword(s):  
Stochastic Analysis ◽  
Beam Structures

Application of wavelets and K-L expansion for stochastic analysis of structures

1997 ◽  
Author(s):  
Mei Hong ◽  
Om Agrawal ◽  
Shantaram Pai ◽  
Mei Hong ◽  
Om Agrawal ◽  
...  
Keyword(s):  
Stochastic Analysis
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