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Moments of random sums and Robbins' problem of optimal stopping
Moments of random sums Robbins' problem Probability
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2011/9/13
Abstract: Robbins' problem of optimal stopping asks one to minimise the expected {\it rank} of observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the {\it value...
Weak and strong moments of random vectors
Weak strong moments random vectors
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2011/1/21
We discuss a conjecture about comparability of weak and strong moments of log-concave random vectors and show the conjectured inequality for unconditional vectors in normed spaces with a bounded cotyp...
Moments Equalities for Nonnegative Integer-Valued Random Variables
Expectation Moments Equalities
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2010/2/26
We present and prove two theorems about equalities for the nth moment of nonnegative integer-valued random variables. These equalities generalize the well known equality for the first moment of a nonn...