Frontiers of Mathematics in China >
Uniform nonintegrability of random variables
Received date: 23 Aug 2016
Accepted date: 24 Nov 2016
Published date: 12 Jan 2018
Copyright
Recently, T. K. Chandra, T. -C. Hu and A. Rosalsky [Statist. Probab. Lett., 2016, 116: 27–37] introduced the notion of a sequence of random variables being uniformly nonintegrable, and presented a list of interesting results on this uniform nonintegrability. We introduce a weaker definition on uniform nonintegrability (W-UNI) of random variables, present a necessary and sufficient condition for W-UNI, and give two equivalent characterizations of WUNI, one of which is a W-UNI analogue of the celebrated de La Vallée Poussin criterion for uniform integrability. In addition, we give some remarks, one of which gives a negative answer to the open problem raised by Chandra et al.
Zechun HU , Xue PENG . Uniform nonintegrability of random variables[J]. Frontiers of Mathematics in China, 2018 , 13(1) : 41 -53 . DOI: 10.1007/s11464-017-0623-6
| 1 |
Chandra T K. De La Vallée Poussin’s theorem, uniform integrability, tightness and moments. Statist Probab Lett, 2015, 107: 136–141
|
| 2 |
Chandra T K, Hu T-C, Rosalsky A. On uniform nonintegrability for a sequence of random variables. Statist Probab Lett, 2016, 116: 27–37
|
| 3 |
Chong K M. On a theorem concerning uniform integrability. Publ Inst Math (Beograd) (NS), 1979, 25(39): 8–10
|
| 4 |
Chow Y S, Teicher H. Probability Theory: Independence, Interchangeability, Martingales.3rd ed. New York: Springer-Verlag, 1997
|
| 5 |
Chung K L. A Course in Probability Theory.2nd ed. New York: Academic Press, 1974
|
| 6 |
Hu T-C, Rosalsky A. A note on the de La Vallée Poussin criterion for uniform integrability. Statist Probab Lett, 2011, 81: 169–174
|
| 7 |
Hu T-C, Rosalsky A. A note on random variables with an infinite absolute first moment. Statist Probab Lett, 2015, 97: 212–215
|
| 8 |
Klenke A. Probability Theory: A Comprehensive Course.2nd ed. London: Springer-Verlag, 2014
|
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