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Invariance principle for martingales on the plane

✍ Scribed by R. Morkvėnas


Publisher
Springer
Year
1984
Tongue
English
Weight
276 KB
Volume
24
Category
Article
ISSN
0363-1672

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Invariance principle for martingale-diff
✍ S. Poghosyan; S. Roelly 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 383 KB

A convergence criterium to the multi-parameter Wiener process is proved. Then, it is used to establish that a martingaledifference random field on the lattice satisfies an invariance principle.

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For continuous local martingales, we establish an almost sure central limit theorem and a logarithmic strong law. We also establish the central limit theorem and the law of iterated logarithm associated with this strong law.