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## Barczy Mátyás: Limit theorems for Bajraktarevic and Cauchy quotient means of independent identically distributed random variables

 Szerda, 4. Szeptember 2019, 14:00 - 16:00
Abstract. We derive strong law of large numbers and central limit theorems for Bajraktarevic and Cauchy quotient means of independent identically distributed (i.i.d.) random variables. The exponential- and logarithmic Cauchy quotient means of a sequence of i.i.d. random variables behave asymptotically normal with the usual square root scaling just like the geometric means of the given random variables. Somewhat surprisingly, the multiplicative Cauchy quotient means of i.i.d. random variables behave asymptotically in a rather different way: in order to get a non-trivial normal limit distribution a time dependent centering is needed. (This is a joint work with Pál Burai.)
Hely : Szeged, Aradi vértanúk tere 1., Riesz terem