2001 m. katedros mokslinio darbo ataskaita

Mokslinio darbo tema: "Funkcini� erdvi� skirstini� analiz� ir jos taikymai statistikoje".

2001 m. gauti rezultatai:

• gauti daugiama�i� stabili�j� d�sni� aproksimacijos Levy-LePage sumomis tikslumo optimal�s �ver�iai. Nagrin�tas mato koncentracijos rei�kinys, gauti kai kurie nauji rezultatai, kurie palyginti su gerai �inomais Talagrand�o rezultatais �ioje srityje;
• sukonstruotas stratifikuot� im�i� be gra�inimo statistik� ortogonalusis skleidinys. Nustatyta stratifikuot� im�i� statistik� d�eknaifo �ver�io poslinkio formul�, �rodyta Efrono-Steino nelygyb�;
• surastos b�tinos ir pakankamos Lampercio invarianti�kumo principo s�lygos. Rastos s�lygos, kada atsitiktinis procesas su reik�m�mis Banacho erdv�je turi hiolderi�k� modifikacij�. Atlikta mok�jimo korteli� transakcij� funkcin� duomen� analiz�, i�nagrin�ta empirinio charakteristinio proceso centrin� ribin� teorema.;
• �rodyta, kad stochastin�s diferencialin�s lygties su pastovia difuzija ir Lip�ico s�lyg� tenkinan�iu poslinkio koeficientu Eulerio aproksimacijos silpn�ja prasme (arba skirstinio prasme) konvergavimo eil� lygi vienam. Gauta pakankama s�lygos stochastin�s eksponent�s p-ojo momento baigtinumui. Parodyta, kad �i s�lyga yra tam tikra prasme nepagerinama.

2001 m. publikacijos �ia tema:

Straipsnis Lietuvos presti�iniame mokslo �urnale:

1. Bloznelis M. Empirical edgeworth expansion for finite population statistics.I. // Lietuvos Matematikos Rinkinys. 2001. Nr. 41(2). P. 154-171.
2. Bloznelis M. Empirical edgeworth expansion for finite population statistics.II. // Lietuvos Matematikos Rinkinys. 2001. Nr. 41(3). P. 263-276.
3. Juozulynas A. Extended classical asymptotic expansions in the case of Gaussian limit distribution // Lietuvos Matematikos Rinkinys. 2001. Nr. 41(2). P. 202-213.
4. Maniu�is V. The new tests for symmetry // Lietuvos Matematikos Rinkinys. 2001. Nr. 41. Specialus numeris. P. 451-456.

1. Bloznelis M., Goetze F. Orthogonal decomposition of finite population statistics and its applications to distributional asymptotics // The Annals of Statistics. 2001. Vol. 29. P. 899-917.
2. Mackevi�ius V. , Navikas J. Second order weak Runge-Kutta type methods for Iti equations // Mathematics and Computers in Simulation. 2001. Vol. 57. P. 29-34.
3. Bentkus V., Juozulynas A., Paulauskas V. Levy-LePage Series Representation of Stable Vectors: Cionvergence in Variation // Journal of Theoretical Probability. 2001. Vol. 14. No.4. P. 949-978.
4. Mittnik S., Paulauskas V., Rachev S.T. Statistical Inference in Regression with Heavy-Tailed Integrated Variables // Mathematical and Computer Modelling. 2001. Vol. 34. P. 1145-1158.
5. Ra�kauskas A., Suquet C. Invariance principles for adaptive self-normalized partial sums processes // Stochastic processes and their applications. 2001. Vol.95. P. 63-81.

1. Ra�kauskas A., Suquet C. Holder versions of Banach space valued random fields // Georgian Mathematical Journal. 2001. Vol. 8. No.2. P.347-362.
2. Ra�kauskas A., G�tze F. Adaptive choice of Bootstrap sample sizes. In: State of the Art in Probability and Statistics (Lecture notes-monograph series). 2001. Vol. 36. P.286-309.

1. Bloznelis M. Orthogonal decomposition of symmetric functions defined on random permutations, Vilnius: VU Matematikos ir informatikos fakultetas, 2001. Preprintas 2001-5.
2. Bloznelis M. Consistency and bias of jackknife variance estimator in stratified samples . Vilnius: VU Matematikos ir informatikos fakultetas, 2001. Preprintas 2001-16.
3. Bloznelis M. A note on the multivariate local limit theorem. Vilnius: VU Matematikos ir informatikos fakultetas, 2001. Preprintas 2001-16.
4. B. Grigelionis, V. Mackevi�ius, The finiteness of moments of a stochastic exponent. VU Matematikos ir informatikos fakultetas, 2001. Preprintas 2001- 35.
5. Mackevi�ius V. On the convergence rate of Euler scheme for SDE with Lipschitz drift and constant diffusion. Vilnius: VU Matematikos ir informatikos fakultetas, 2001. Preprintas 2001- 34.
6. Norvidas S. Polynomial Bernstein's inequalities. Vilnius: VU Matematikos ir informatikos fakultetas, 2001. Preprintas 2001-33.
7. Ra�kauskas A., Suquet Ch. H�lder convergences of multivariate empirical characteristic functions. Pranc�zija: Pub. IRMA, Lille, 2001. 54. VI.

1. Bloznelis M. Orthogonal decomposition of combinatorial statistics. Conf. �Stochastic analysis and its applications�. Lviv 2001, June10-17. Lviv University Press. P. 6.
2. Ra�kauskas A. On adaptive selfnormalized partial sums process. European Working Group on Financial Modeling, 28th Workschop in Vilnius. Vilnius, 2001 May 3-5, p.28.
3. Ra�kauskas A. , Suquet Ch., Convergence of self-normalized partial sums processes in Holder spaces, XXI Seminar on Stability Problems of Stochastic Models, Eger, 28 January - 3 February, 2001; Abstracts, p. 154 -155.

1. Maniu�is V. Nauji skirstini� simetri�kumo testai (The new tests for symmetry). Lietuvos matematik� draugijos XLII konferencija. Klaip�dos universitetas, Klaip�da, 2001 m. bir�elio 22-23 d.
2. Ra�kauskas A. Tankio �vertinim� skirstini� butstrepin�s aproksimacijos (Bootstrap approximation of distribution of density estimate). Lietuvos matematik� draugijos XLII konferencija. Klaip�dos universitetas, 2001 m. bir�elio 22-23 d. (2001)
3. Sku�ait� A., Baltr�nas A. Asimptotiniai dideli� nuokrypi� tikimybi� rezultatai ir taikymas perdraudime (Some asymptotic results for large deviation one sided probabilities with applications to reinsurance). Lietuvos matematik� draugijos XLII konferencija. Klaip�dos universitetas, 2001 m. bir�elio 22-23 d. (2001).

1. Bloznelis M. Orthogonal decomposition of symmetric functions defined on random permutations (Simetrini� atsitiktini� k�lini� funkcij� ortogonalieji skleidiniai). Conf. �Atsitiktines strukt�ros ir algoritmai 2001�, 2001 August 6-10, Poznan�, Lenkija.
2. M. Bloznelis. Orthogonal decomposition of combinatorial statistics. �Asymptotic combinatorics with application to mathematical physics� 2001 July 9-23, Peterburgas, Rusija.
3. Paulauskas V. On random sets and cantor type sets on a line. The III International Conference �Analytic and Probabilistic Methods in Number Theory�. Palanga (Lietuva), September 24-28. (2001). Dedicated to the 80th birthday of Professor Jonas Kubilius.
4. Paulauskas V. On some new results for multivariate stable laws. Conf. �Stable processes, laws and applications�. Oberwolfach (Germany), 2001, October 28-November 03.
5. Zov� R. Hausdorf dimension of Cantor-type sets on a plane. The III International Conference �Analytic and Probabilistic Methods in Number Theory�. Palanga (Lietuva), September 24-28. (2001). Dedicated to the 80th birthday of Professor Jonas Kubilius.