ANNALES
UNIVERSITATIS MARIAE CURIE-SKŁODOWSKA
SECTIO A
MATHEMATICA
VOL. L I . 1 LUBLIN 1997
uinhi inniinin u i u i u i n i u i n. ui iiiiini i u i n i mu 1111 u ...11 ■ 11111111111i n • 11 11i■ 111u 1111111.111111i ■ 11 ■. 11i111 n 11111n ii11111111n 11 n ■ n...11111111 ■ 111.1.n i u i■ i.■ ■ i ■ 1 ... ...mu...11111111111 u 111111 u 1111 u 11 n 11111 ■111 ■I ■ 111...miniin u
UNIWERSYTET MARII CURIE-SKŁODOWSKIEJ
ISSN 0365-1029
egzemplarz obowiązkowy
bibliotekaUMCS lublin
The papers in this volume are dedicated to Professor Dominik Szy
nal, on the occasion of his sixtieth birthday, by his friends, students, and colleagues.
Dominik Szynal is the founder of the Lublin centre of research in prob
ability, a man whose creative insight has substantially advanced the devel
opment of the theory of probability. He is also an outstanding teacher and many students were helped and guided by him to their best interests.
Happy Birthday to you, Dominik!
Jan G. Krzyż and Zdzisław Rychlik
ANNALES
UN IV ER S IT ATI S MARIAE CUR IE-S KŁODO WS KA
KOM
CBvteO S1V|
ITET REDAKC'YJNY
REDAKTOR NACZELNY
Grzegorz Leopold Seidler
ZASTĘPCY REDAKTORA NACZELNEGO
Wiesław Skrzydło, Wiesław Śladkowski
REDAKTORZY SEKCJI
A MATHEMATICA Adam Bielecki, Jan Krzyż AA CHEMIA Kazimierz Sykut AAA PHYSICA Jan Sielewiesiuk
B GEOGRAPHIA,
GEOLOGIA ETC. Józef Wojtanowicz C BIOLOGIA Zbigniew Lorkiewicz D MEDICINA Stanisław Bryc DD MEDICINA
VETERINARIA Zdzisław Gliński DDD PHARMACIA Romuald Langwiński
E AGRICULTURA Adam Szember EE ZOOTECHNICA Marian Budzyński EEE HORTICULTURA Maria Tendaj
F HISTORIA Wiesław Śladkowski FF PHILOLOGIAE Alina Aleksandrowicz
G IUS Wiesław Skrzydło
Antoni Pieniążek - zastępca redaktora H OECONOMIA Ryszard Orłowski
I PHILOSOPHIA
- SOCIOLOG1A Zdzisław Cackowski J PAEDAGOGIA
- PSYCHOLOGIA Stanisław Popek K POLITOLOGIA Jan Jachymek
ANNALES UNIVERSITATIS MARIAE CURIE-SKŁODOWSKA
SECTIO A
MATHEMATICA
V O L. L 1. 1 LUBLIN 1997
■iii iniiiinniiii ...uiini i ni u i nhini i ...nimin in un urn...ii... i. u i.. 11.1 ■ i ■ u 1111 n 111 mim iii.ihi i...nu... ... ...i... ...mu ... . u i u i n 11 • i u i u i u in i n 1111 ii ... .
UNIWERSYTET MARII CURIE-SKŁODOWSKIEJ ISSN 0365-1029
REDAKTOR TOMU
JAN KRZYŻ
PROJEKT OKŁADKI 1 STRON TYTUŁOWYCH
JERZY DURAKIEWICZ
SEKRETARZ REDAKCJI
LECH MALISZEWSKI
REDAKCJA WYDAWNICZA
I SKŁAD SYSTEMEM TfcX
JADWIGA ZYGMUNT
ISSN 0365-1029
WYDAWNICTWO UNIWERSYTETU MARII CURIE-SKLODOWSKIEJ PI. Marii Curie-Sklodowskiej 5, 20-031 Lublin, lei. (0-81) 537-53-02, 537-53-04
DRUK: ZAKŁAD POLIGRAFII WYDAWNICTWA UMCS
ANNALES
U NIV E RS IT A TIS MARIAE C U RIE - S K Ł O D O W S K A LUBLIN - POLONIA
VOL. LI.l SECTIO A 1997
Table of contents
Dominik Szynal - A Biography List of publications
1. ROBERT BARTOSZYŃSKI, PREM K. GOEL On Probability of Evens
2. AGATA BORATYŃSKA, RYSZARD ZIELIŃSKI
Asymptotic Behavior of Sample Median in a Parametric Model 3. SANDOR CSÓRGÓ
Renyi-Mixing in the Generalized Arc-Sine Law 4. DOROTA DUDEK, WIESŁAW ZIĘBA
A Note on the Strong Tightness in C[0, 1]
5. RICHARD DUNCAN
Weak Convergence of Spectral Measures 6. LESŁAW GAJEK, ANDRZEJ OKOLEWSKI
Steflensen-type Inequalities for Order and Record Statistics 7. SYLWIA GUTKOWSKA, WIESŁAW ZIĘBA
On a Stability in Renyi’s Sense
8. EWA HENSZ-CHĄDZYŃSKA, RYSZARD JAJTE, ADAM PASZKIEWICZ
Almost Sure Convergence of Projections in Lp-Spaces 9. T. C. HU, A. I. VOLODIN
Complete Convergence Criterion for Arrays of Banach Space Valued Random Elements
10. ZBIGNIEW J. JUREK
Selfdecomposability: an Exception or a Rule ?
vii ix
1
11
15
27
35
41
61
67
85
93
11. PIOTR KOWALSKI, ZDZISŁAW RYCHLIK
On the Weak Law of Large Numbers for Randomly
Indexed Partial Sums for Arrays 109
12. WŁODZIMIERZ KRYSICKI
The Density of a Three-parameter Random Variable with the Gamma Distribution as the Density of a Finite or Infinite Product 121 13. PRZEMYSŁAW MATULA
The Glivenko-Cantelli Lemma for a Class of Discrete
Associated Random Variables 129
14. JOANNA NOWICKA, ALEKSANDER WERON
Measures of Dependence for ARMA Models with Stable Innovations 133 15. KAZIMIERZ SOBCZYK
On Cumulative Jump Models for Random Deterioration Processes 145 16. JÓZEF L. TEUGELS
On the Pólya-Eggenberger Distribution and its Applicability
in Insurance Mathematics 159
17. KAZIMIERZ URBANIK
Multiplicative Decomposability of Probability Measures 173 18. JERZY ZABCZYK
Stopping Problems on Polish Spaces 181
19. AUGUST M. ZAPALA
On the Inversion Formula for Probability Densities 201
