Moderate deviation principles for sums of i.i.d. random compact sets
Commentationes Mathematicae Universitatis Carolinae (2009)
- Volume: 50, Issue: 1, page 103-111
- ISSN: 0010-2628
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topMiao, Yu. "Moderate deviation principles for sums of i.i.d. random compact sets." Commentationes Mathematicae Universitatis Carolinae 50.1 (2009): 103-111. <http://eudml.org/doc/32484>.
@article{Miao2009,
abstract = {We prove a moderate deviation principle for Minkowski sums of i.i.d. random compact sets in a Banach space.},
author = {Miao, Yu},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {moderate deviation; random sets; moderate deviation; random set},
language = {eng},
number = {1},
pages = {103-111},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Moderate deviation principles for sums of i.i.d. random compact sets},
url = {http://eudml.org/doc/32484},
volume = {50},
year = {2009},
}
TY - JOUR
AU - Miao, Yu
TI - Moderate deviation principles for sums of i.i.d. random compact sets
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2009
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 50
IS - 1
SP - 103
EP - 111
AB - We prove a moderate deviation principle for Minkowski sums of i.i.d. random compact sets in a Banach space.
LA - eng
KW - moderate deviation; random sets; moderate deviation; random set
UR - http://eudml.org/doc/32484
ER -
References
top- Artstein Z., Vitale R.A., A strong law of large numbers for random compact sets, Ann. Probability (1975), 3 879--882. (1975) Zbl0313.60012MR0385966
- Chen X., Probabilities of moderate deviations for independent random vectors in a Banach space, Chinese J. Appl. Prob. Stat. (1991), 7 24--32. (1991) MR1204537
- Chen X., 10.1016/S0167-7152(97)00005-9, Statist. Probab. Lett. (1997), 35 123--134. (1997) Zbl0887.60010MR1483265DOI10.1016/S0167-7152(97)00005-9
- Cerf R., Large deviations for sums of i.i.d. random compact sets, Proc. Amer. Math. Soc. (1999), 127 8 2431--2436. (1999) Zbl0934.60017MR1487361
- Dembo A., Zeitouni O., Large Deviations Techniques and Applications, second edition, Springer, New York, 1998. Zbl0896.60013MR1619036
- Deuschel J.D., Stroock D.W., Large Deviations, Pure and Applied Mathematics, 137, Academic Press, Boston, MA, 1989. Zbl0791.60017MR0997938
- Dunford N., Schwartz J.T., Linear Operators. Part I: General Theory, Interscience Publishers, New York-London, 1958. Zbl0635.47001MR1009162
- Giné E., Hahn M.G., Zinn J., Limit theorems for random sets: an application of probability in Banach space results, Probability in Banach Spaces IV (Oberwolfach, 1982), Springer, Berlin, 1983, pp. 112--135. MR0707513
- Puri M.L., Ralescu D.A., Limit theorems for random compact sets in Banach space, Math. Proc. Cambridge Philos. Soc. (1985), 97 151--158. (1985) Zbl0559.60007MR0764504
- Rudin W., Real and Complex Analysis, McGraw-Hill, New York, 1966. Zbl1038.00002MR0210528
- Rudin W., Functional Analysis, McGraw-Hill, New York, 1973. Zbl0867.46001MR0365062
- Wu L.M., An introduction to large deviations, in Several Topics in Stochastic Analysis (J.A. Yan, S. Peng, S. Fang and L. Wu, Eds.), pp. 225--336, Academic Press of China, Beijing, 1997 (in Chinese). Zbl0575.60032
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