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Office address:

 Vilnius University,
Faculty of Mathematics and Informatics,  Naugarduko 24,
Vilnius, 2006, Lithuania

Phone +370 -5- 2336022
Fax   +370 -5- 2151585
E-mail mblozn@ieva.maf.vu.lt


TEACHING 2002/2003 ACADEMIC YEAR

"Randomized Algorithms"  -------> Fall semester,    master students (Informatics ), 2 credits

"Actuarial Mathematics"  -------> Fall semester,   bachelor students (Mathematics), 3 credits

"Probability Theory" ---------->     Spring semester, bachelor students (Econometrics), 3 credits

"Combinatorics and graph theory" ---------->  Spring semester, bachelor students
(Econometrics and financial mathematics), 3 credits

"Risk theory and non-life insurance mathematics" -----------> Spring semester,
 bachelor students (Financial mathematics), 3 credits


RESEARCH

Probability limit theorems (research papers [1-4], [13], [17,18], [20], [32] )

----------->  My research in the field of probability limit theorems focuses on the
convergence rate of distributions of sums of independent and identically distributed random
variables (and random vectors) to stable distributions.  The main achievement is the so called
"non-uniform bound" for the convergence rate.


Limit theorems for random processes (research papers [4-12], [14-16], [19], [27], [32])
---------->Main results establish sufficient conditions for the central limit theorem  to hold
for stochastically continuous random processes in Skorokhod space D[0,1]
of CADLAG (right continuous and having left limits) functions. The case of
 Gaussian limit process (with continuous sample paths) and the case of stochastically continuous
 stable limit process (with sample paths having no discontinuities of the second kind) are
 treated separately. Conditions are formulated in terms of moments (weak moments in case of
 stable limit) of increments of summands (that are stochastically continuous processes with
 sample paths in D[0,1]).



Mathematical statistics: approximation of distributions of non-linear statistics
(research papers [17,18], [20,21], [33])
--------------------> A new approach is used to study the accuracy of the normal approximation
of M estimators in the case of asymptotically convex score function, see [18].
This approach (based on the law of large numbers for random functions) allows to show a
Berry-Esseen bound under optimal conditions (minimal smoothness condition on the score function
and optimal moment conditions).
Accuracy of the normal approximation of distributions selfnormalized sums is studied in
 [17], [20,21]. A general and precise Berry-Esseen type bound for Student's t statistic is
 shown in [17] for independent not identically distributed observations. One term Edgeworth
 expansion is established in [20,21] under the optimal conditions: finite third moment and
 non-lattice distribution of summands.


Mathematical statistics: approximation of distributions of finite population statistics
(research papers [22-26], [28-31], [34-37])
--------------> The papers [22,24, 30,31] develop  Hoeffding's decomposition for symmetric
statistics and show one term Edgeworth expansion for distributions of symmetric statistics.
Empirical Edgeworth expansion (based on jackknife estimators of moments defining the expansion)
is constructed in [28,29]. One term Edgeworth expansion and its empirical counterpart is constructed
for Studentized finite population statistics in [35,37].
Stratified samples are considered in [34,36].


CURRENT RESEARCH
------------->

normal approximation and Edgeworth expansions for distributions of symmetric statistics;

resampling approximation in finite populations;

approximations of distributions of combinatorial statistics (sub-graph count).


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Curriculum Vitae


 ACADEMIC DEGREES OBTAINED

1986 University Diploma, Vilnius University (Mathematics)


1990 Candidate of Sciences degree, Vilnius University (Probability
Theory)


2000 Habilitation, Vilnius University (Probability Theory and Mathematical
Statistics)



  PROFESSIONAL BACKGROUND

1. Vilnius University (Lithuanian state university)


 1986-1988 assistant


 1988-1990 Ph.D student


  1990-1992 assistant


1992-1996 senior assistant


1996-2001 docent (associated professor)



2001- full professor


 2002 appointed head of Mathematical computer science department.



2. Institute of mathematics and Informatics (Lithuanian state science institute)




1993-1996 research fellow

1996- 2001 senior research fellow

2001-  principal research fellow



  STUDIES AND RESEARCH ABROAD


1994  Bielefeld University and J.W.Goethe University in
Frankfurt/M, Germany;

 Institute of Automation and Information in
Prague, Czech Republics;

1995 Bielefeld University, Germany;

1996 Helsinki University, Finland; Bielefeld University, Germany;

1997 Bielefeld University, Germany; Leiden University, The Netherlands;

1998, 1999 Alexander von Humbold fellowship, Germany (Bielefeld
University);

2000 Bielefeld University, Germany; CWI Amsterdam, The Netherlands;

2001 Bielefeld University, Germany; Lille 1 University, France;

2002 Bielefeld University, Germany.


INVITED LECTURES

1.Title: "A new non-uniform Berry-Esseen type bound in the case of stable limiting
laws".
 Conference: "Limit Theorems and Nonparametric Statistics"
1992 Bielefeld University, Germany.

2. Title: "Resampling for finite populations".
 Conference:
"Baltic-Nordic conference on survey sampling" 2002,
 Umea university, Ammarnas, Sweden.



 AWARDS

Lithuanian State Science prize 2003;

Alexander fon Humboldt Research Fellowship, Germany, 1999;

Lithuanian Academy of Sciences "Young scientists prize" 1995.


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