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5 papers · 2 filters
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…
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 \…
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{…
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…
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…