On non-differentiable measure-preserving functions

1990 ◽  
Vol 16 (1) ◽  
pp. 119 ◽  
Author(s):  
Bobok
Keyword(s):  
Differentiable Measure

scholarly journals SMOOTH PROBABILITY MEASURES AND ASSOCIATED DIFFERENTIAL OPERATORS

1999 ◽  
Vol 02 (01) ◽  
pp. 51-78 ◽  
Author(s):  
O. G. SMOLYANOV ◽  
H. v. WEIZSÄCKER
Keyword(s):  
Differential Operators ◽  
Finite Dimensional ◽  
Differentiable Measure ◽  
Chaos Decomposition ◽  
Gaussian Case ◽  
Non Gaussian ◽  
Associated Differential Operators ◽  
Locally Convex ◽  
Nonsmooth Mappings

We compare different notions of differentiability of a measure along a vector field on a locally convex space. We consider in the L2-space of a differentiable measure the analog of the classical concepts of gradient, divergence and Laplacian (which coincides with the Ornstein–Uhlenbeck operator in the Gaussian case). We use these operators for the extension of the basic results of Malliavin and Stroock on the smoothness of finite dimensional image measures under certain nonsmooth mappings to the case of non-Gaussian measures. The proof of this extension is quite straight forward and does not use any Chaos-decomposition. Finally, the role of this Laplacian in the procedure of quantization of anharmonic oscillators is discussed.

scholarly journals BV functions in a Gelfand triple for differentiable measure and its applications

2015 ◽  
Vol 27 (3) ◽  
Author(s):  
Michael Röckner ◽  
Rongchan Zhu ◽  
Xiangchan Zhu
Keyword(s):  
Dirichlet Form ◽  
Adjoint Operator ◽  
Stochastic Quantization ◽  
Bv Functions ◽  
Form Theory ◽  
Differentiable Measure ◽  
Definition Of ◽  
Non Gaussian ◽  
Gelfand Triple ◽  
Quantization Problem

AbstractIn this paper, we introduce a definition of BV functions for (non-Gaussian) differentiable measure in a Gelfand triple which is an extension of the definition of BV functions in [Ann. Probab. 40 (2012), 1759–1794], using Dirichlet form theory. By this definition, we can analyze the reflected stochastic quantization problem associated with a self-adjoint operator

scholarly journals Introducing a differentiable measure of pointwise shared information

2021 ◽  
Vol 103 (3) ◽  
Author(s):  
Abdullah Makkeh ◽  
Aaron J. Gutknecht ◽  
Michael Wibral
Keyword(s):  
Shared Information ◽  
Differentiable Measure
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