Tail and moment estimates for chaoses generated by symmetric random variables with logarithmically concave tails

Abstract

We present two-sided estimates of moments and tails of polynomial chaoses of\norder at most three generated by independent symmetric random variables with\nlog-concave tails as well as for chaoses of arbitrary order generated by\nindependent symmetric exponential variables. The estimates involve only\ndeterministic quantities and are optimal up to constants depending only on the\norder of the chaos variable.\n