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math.PR2011★ 32 cited

The rate of convergence of estimate for Hurst index of fractional Brownian motion involved into stochastic differential equation

K. Kubilius, Y. Mishura

We consider stochastic differential equation involving pathwise integral with respect to fractional Brownian motion. The estimates for the Hurst parameter are constructed according…

math.PR2011

Bounds for tail probabilities of martingales using skewness and kurtosis

Vidmantas Bentkus, Tomas Juškevičius

Let $M_n= \fsu X1n$ be a sum of independent random variables such that , $\E X_k =0$ and $\E X_k^2=\s_k^2$ for all . Hoeffding 1963, Theorem 3, proved that $$¶{M_n \…

math.PR2011★ 7 cited

Optimal Probability Inequalities for Random Walks related to Problems in Extremal Combinatorics

Dainius Dzindzalieta, Matas Šileikis, Tomas Juškevičius

Let S_n=X_1+...+X_n be a sum of independent symmetric random variables such that |X_{i}|\leq 1. Denote by W_n=ε_{1}+...+ε_{n} a sum of independent random variables such that \prob{…

math.PR2011★ 11 cited

Weighted power variation of integrals with respect to a Gaussian process

Rimas Norvaiša

We consider a stochastic process defined by an integral in quadratic mean of a deterministic function with respect to a Gaussian process , which need not have stationary…

math.PR2011★ 10 cited

Once more on comparison of tail index estimators

Vygantas Paulauskas, Marijus Vaičiulis

We consider heavy-tailed distributions and compare the well-known estimators of the tail index, based on extreme value theory with a comparatively recent estimator based on a diffe…