Bilateral tail estimate for distribution of self normalizes sums of independent centered random variables under natural norming

Abstract

We derive in this article the exact non-asymptotical exponential and power estimates for self-normalized sums of centered independent random variables (r.v.) under natural norming. We will use also the theory of the so-called Grand Lebesgue Spaces (GLS) of random variables.

References in corpus (3)

• Schlomilch and Bell Series for Bessel's Functions, with Probabilistic Applications
• Vector rearrangement invariant banach spaces of random variables with exponential decreasing tails of distributions
• Sharp moment estimates for polynomial martingales