scholarly journals Absolute continuity and singularity of probability measures induced by a purely discontinuous Girsanov transform of a stable process

2016 ◽  
Vol 369 (3) ◽  
pp. 1547-1577 ◽  
Author(s):  
René L. Schilling ◽  
Zoran Vondraček
Keyword(s):  
Absolute Continuity ◽  
Stable Process ◽  
Probability Measures ◽  
Girsanov Transform

ON THE QUESTION OF ABSOLUTE CONTINUITY AND SINGULARITY OF PROBABILITY MEASURES

1977 ◽  
Vol 33 (2) ◽  
pp. 203-221 ◽  
Author(s):  
Ju M Kabanov ◽  
R Š Lipcer ◽  
A N Širjaev
Keyword(s):  
Absolute Continuity ◽  
Probability Measures

scholarly journals Rearranging measures

1983 ◽  
Vol 34 (1) ◽  
pp. 16-30 ◽  
Author(s):  
G. Brown ◽  
J. H. Williamson
Keyword(s):  
Absolute Continuity ◽  
Infinite Sequence ◽  
Probability Measures ◽  
Stieltjes Transforms

AbstractA churning transformation can be defined on probability measures by an infinite sequence of finite permutations of mass. Continuity and absolute continuity of measures are invariants for such transformations but it is shown that certain probability measures whose Fourier-Stieltjes transforms fail to vanish at infinity may be churned into measures whose transforms do vanish in this sense.

scholarly journals On absolute continuity and singularity of probability measures

1980 ◽  
Vol 6 (1) ◽  
pp. 121-132 ◽  
Author(s):  
H. Engelbert ◽  
A. Shiryaev
Keyword(s):  
Absolute Continuity ◽  
Probability Measures

scholarly journals Formulation and properties of a divergence used to compare probability measures without absolute continuity

2022 ◽  
Author(s):  
Paul Dupuis ◽  
Yixiang Mao
Keyword(s):  
Relative Entropy ◽  
Model Uncertainty ◽  
Absolute Continuity ◽  
Optimal Transport ◽  
Transport Cost ◽  
Probability Measures

This paper develops a new divergence that generalizes relative entropy and can be used to compare probability measures without a requirement of absolute continuity. We establish properties of the divergence, and in particular derive and exploit a representation as an infimum convolution of optimal transport cost and relative entropy.  Also included are examples of computation and approximation of the divergence, and the demonstration of properties that are useful when one quantifies model uncertainty.

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