Power variations for fractional type infinitely divisible random fields

This paper presents new limit theorems for power variations of fractional type symmetric infinitely divisible random fields. More specifically, the field X=(X(t))t?[0,1]d is defined as an integral a kernel function g with respect to measure L and observed on grid mesh size n?1. As n??, first order limits are obtained variation statistics constructed from rectangular increments X. The present work mostly related [8, 9], who studied similar problem in case d=1. We will see, however, that asymptotic theory setting much richer compared 9] it contains limits, which depend precise structure g. give some important examples including Lévy moving average field, well-balanced linear ?-stable sheet, discuss potential consequences statistical inference.