Choquet-type integral representation of polysupermedian measures

1994 ◽  
Vol 3 (4) ◽  
pp. 359-378
Author(s):  
K. Janssen
Keyword(s):  
Integral Representation ◽  
Type Integral

FURSTENBERG-TYPE FORMULAS OVER SHIFT SPACES

2003 ◽  
Vol 03 (04) ◽  
pp. 499-527
Author(s):  
SUSANNE KOCH
Keyword(s):  
Markov Chains ◽  
Integral Representation ◽  
Harmonic Functions ◽  
Type Formula ◽  
Shift Spaces ◽  
Type Integral ◽  
Self Similar

We define a class of Markov chains of unbounded range on word spaces and deduce a Furstenberg-type integral representation for a subspace of the P-harmonic functions. As an application we obtain a Furstenberg-type formula for a set of continuous harmonic functions on p.c.f. self-similar sets.

Relations Between Hidden Regular Variation and the Tail Order of Copulas

2014 ◽  
Vol 51 (01) ◽  
pp. 37-57 ◽  
Author(s):  
Lei Hua ◽  
Harry Joe ◽  
Haijun Li
Keyword(s):  
Integral Representation ◽  
Random Vector ◽  
Regular Variation ◽  
Dependence Structure ◽  
Multivariate Regular Variation ◽  
Intensity Measures ◽  
Extremal Dependence ◽  
Measure Representation ◽  
Hidden Regular Variation ◽  
Type Integral

We study the relations between the tail order of copulas and hidden regular variation (HRV) on subcones generated by order statistics. Multivariate regular variation (MRV) and HRV deal with extremal dependence of random vectors with Pareto-like univariate margins. Alternatively, if one uses a copula to model the dependence structure of a random vector then the upper exponent and tail order functions can be used to capture the extremal dependence structure. After defining upper exponent functions on a series of subcones, we establish the relation between the tail order of a copula and the tail indexes for MRV and HRV. We show that upper exponent functions of a copula and intensity measures of MRV/HRV can be represented by each other, and the upper exponent function on subcones can be expressed by a Pickands-type integral representation. Finally, a mixture model is given with the mixing random vector leading to the finite-directional measure in a product-measure representation of HRV intensity measures.

scholarly journals Relations Between Hidden Regular Variation and the Tail Order of Copulas

2014 ◽  
Vol 51 (1) ◽  
pp. 37-57 ◽  
Author(s):  
Lei Hua ◽  
Harry Joe ◽  
Haijun Li
Keyword(s):  
Integral Representation ◽  
Random Vector ◽  
Regular Variation ◽  
Dependence Structure ◽  
Multivariate Regular Variation ◽  
Intensity Measures ◽  
Extremal Dependence ◽  
Measure Representation ◽  
Hidden Regular Variation ◽  
Type Integral

We study the relations between the tail order of copulas and hidden regular variation (HRV) on subcones generated by order statistics. Multivariate regular variation (MRV) and HRV deal with extremal dependence of random vectors with Pareto-like univariate margins. Alternatively, if one uses a copula to model the dependence structure of a random vector then the upper exponent and tail order functions can be used to capture the extremal dependence structure. After defining upper exponent functions on a series of subcones, we establish the relation between the tail order of a copula and the tail indexes for MRV and HRV. We show that upper exponent functions of a copula and intensity measures of MRV/HRV can be represented by each other, and the upper exponent function on subcones can be expressed by a Pickands-type integral representation. Finally, a mixture model is given with the mixing random vector leading to the finite-directional measure in a product-measure representation of HRV intensity measures.

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