Strong Law of Large Numbers for Adapted Sequences and Application to Multivalued Supermartingale

Strong Law of Large Numbers for Adapted Sequences and Application to Multivalued Supermartingale

In this paper, we prove the strong law of large numbers (SLLN) for a real adapted sequence. As application, we establish the relation between SLLN and amart and also we prove the strong law of large numbers for mils. At the end of this work, the SLLN for set valued supermartingale is provided.

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Veröffentlicht in:Lobachevskii journal of mathematics 2020-03, Vol.41 (3), p.407-415
Hauptverfasser: Oulghazi, H., Ezzaki, F.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Analysis
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
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Zusammenfassung:In this paper, we prove the strong law of large numbers (SLLN) for a real adapted sequence. As application, we establish the relation between SLLN and amart and also we prove the strong law of large numbers for mils. At the end of this work, the SLLN for set valued supermartingale is provided.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080220030142