On some definition of expectation of random element in metric space

Artur Bator; Wiesław Zięba

Annales UMCS, Mathematica (2009)

  • Volume: 63, Issue: 1, page 39-48
  • ISSN: 2083-7402

Abstract

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We are dealing with definition of expectation of random elements taking values in metric space given by I. Molchanov and P. Teran in 2006. The approach presented by the authors is quite general and has some interesting properties. We present two kinds of new results:• conditions under which the metric space is isometric with some real Banach space;• conditions which ensure "random identification" property for random elements and almost sure convergence of asymptotic martingales.

How to cite

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Artur Bator, and Wiesław Zięba. "On some definition of expectation of random element in metric space." Annales UMCS, Mathematica 63.1 (2009): 39-48. <http://eudml.org/doc/268117>.

@article{ArturBator2009,
abstract = {We are dealing with definition of expectation of random elements taking values in metric space given by I. Molchanov and P. Teran in 2006. The approach presented by the authors is quite general and has some interesting properties. We present two kinds of new results:• conditions under which the metric space is isometric with some real Banach space;• conditions which ensure "random identification" property for random elements and almost sure convergence of asymptotic martingales.},
author = {Artur Bator, Wiesław Zięba},
journal = {Annales UMCS, Mathematica},
keywords = {Convex combination; metric space; Banach space; martingale; amart; convex combination},
language = {eng},
number = {1},
pages = {39-48},
title = {On some definition of expectation of random element in metric space},
url = {http://eudml.org/doc/268117},
volume = {63},
year = {2009},
}

TY - JOUR
AU - Artur Bator
AU - Wiesław Zięba
TI - On some definition of expectation of random element in metric space
JO - Annales UMCS, Mathematica
PY - 2009
VL - 63
IS - 1
SP - 39
EP - 48
AB - We are dealing with definition of expectation of random elements taking values in metric space given by I. Molchanov and P. Teran in 2006. The approach presented by the authors is quite general and has some interesting properties. We present two kinds of new results:• conditions under which the metric space is isometric with some real Banach space;• conditions which ensure "random identification" property for random elements and almost sure convergence of asymptotic martingales.
LA - eng
KW - Convex combination; metric space; Banach space; martingale; amart; convex combination
UR - http://eudml.org/doc/268117
ER -

References

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  11. Kruk, Ł., Zięba, W., On tightness of randomly indexed sequences of random elements, Bull. Polish Acad. Sci. Math. 42 (1994), 237-241. Zbl0830.60007
  12. Pick, R., Expectation in metric spaces, Studia Sci. Math. Hungar. 22 (1987), 347-350. Zbl0658.60009
  13. Sturm, K. T., Nonlinear martingale theory for processes with values in metric spaces of nonpositive curvature, Ann. Probab. 30 (2002), 1195-1222. Zbl1017.60050
  14. Terán, P., Molchanov, I., The law of large numbers in a metric space with a convex combination operation, J. Theoret. Probab. 19 (2006), 875-897. Zbl1113.60014
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