Summary
In [4] Zheng Wei-an showed that Fatou's Lemma as presented in the book by Liptser and Shiryayev does not hold true. This paper presents a condition under which this Lemma does hold true.
References
Liptser, R.S., Shiryayev, A.N.: Statistics of Random Processes I. Berlin Heidelberg New York: Springer 1978
Neveu, J.: Discrete-parameter martingales. Amsterdam New York: Elsevier 1975
Szynal, D., Zieba, W.: On some characterization of almost sure convergence. Bull. Acad. Polon. Sci. Ser. Sci. Math.34, 635–642 (1986)
Zheng, Wei-an.: A note on the convergence of sequence of conditional expectations of random variables. Z. Wahrscheinlichkeitstheor. Verw. Geb.53, 291–292 (1980)
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Zieba, W. A note on conditional Fatou Lemma. Probab. Th. Rel. Fields 78, 73–74 (1988). https://doi.org/10.1007/BF00718036
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DOI: https://doi.org/10.1007/BF00718036
Keywords
- Stochastic Process
- Probability Theory
- Mathematical Biology
- Fatou Lemma