We show that the accumulated gain Sn and the maximal gain Mn in n St. Petersburg games satisfy almost sure limit theorems with nondegenerate limits, even though ordinary asymptotic distributions do not exist for Sn and Mn with any numerical centering and norming sequences.
Almost sure limit theorems for the maximum of stationary Gaussian sequences
✍ Scribed by Endre Csáki; Khurelbaatar Gonchigdanzan
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 111 KB
- Volume
- 58
- Category
- Article
- ISSN
- 0167-7152
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✦ Synopsis
We prove an almost sure limit theorem for the maxima of stationary Gaussian sequences with covariance r n under the condition r n log n(log log n) 1+ = O(1).
📜 SIMILAR VOLUMES
We extend the almost sure max-limit theorem to the case of unbounded functions.
## Abstract Let {__S~n~__, __n__ ≥ 1} be partial sums of independent identically distributed random variables. The almost sure version of CLT is generalized on the case of randomly indexed sums {__S~Nn~__, __n__ ≥ 1}, where {__N~n~__, __n__ ≥ 1} is a sequence of positive integer‐valued random varia
In this paper we consider two functional limit theorems for the non-linear functional of the stationary Gaussian process satisfying short range dependence conditions: the functional CLT for partial sum processes and the uniform CLT for a special class of functions. To carry out the proofs, we develo