✦ LIBER ✦
Strong laws for the maximal gain over increasing runs
✍ Scribed by Andrei Frolov; Alexander Martikainen; Josef Steinebach
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 107 KB
- Volume
- 50
- Category
- Article
- ISSN
- 0167-7152
No coin nor oath required. For personal study only.
✦ Synopsis
Let {(Xi; Yi)}i=1;2;::: be an i.i.d. sequence of bivariate random vectors with P(Y1 = y) = 0 for all y. Put Mn = Mn(Ln) = max 06k6n-Ln (X k+1 +
denotes the indicator function of the event in brackets, Ln is the largest '6n, for which I k; ' = 1 for some k = 0; 1; : : : ; n -'. If, for example, Xi = Yi; i¿1, and Xi denotes the gain in the ith repetition of a game of chance, then Mn is the maximal gain over increasing runs of maximal length Ln. We derive a strong law of large numbers and a law of iterated logarithm type result for Mn.