Research output: Contribution to journal › Article › peer-review
Unified limit theorems for increments of processes with independent increments. / Frolov, A. N.
In: Theory of Probability and its Applications, Vol. 49, No. 3, 2005, p. 531-540.Research output: Contribution to journal › Article › peer-review
}
TY - JOUR
T1 - Unified limit theorems for increments of processes with independent increments
AU - Frolov, A. N.
N1 - Copyright: Copyright 2012 Elsevier B.V., All rights reserved.
PY - 2005
Y1 - 2005
N2 - A unified theory is constructed which describes the a.s. (almost surely) behavior of increments of stochastically continuous homogeneous processes with independent increments. This theory includes the strong law of large numbers, the Erdös-Rényi law, the Shepp law, the Csörgo- Révész law, and the law of the iterated logarithm. The range of applicability of the results is extended from several particular cases to the whole class of stochastically continuous homogeneous processes with independent increments.
AB - A unified theory is constructed which describes the a.s. (almost surely) behavior of increments of stochastically continuous homogeneous processes with independent increments. This theory includes the strong law of large numbers, the Erdös-Rényi law, the Shepp law, the Csörgo- Révész law, and the law of the iterated logarithm. The range of applicability of the results is extended from several particular cases to the whole class of stochastically continuous homogeneous processes with independent increments.
KW - Erdös-Rényi law
KW - Increments of processes with independent increments
KW - Shepp law
KW - The law of large numbers
KW - The law of the iterated logarithm
UR - http://www.scopus.com/inward/record.url?scp=27144433814&partnerID=8YFLogxK
U2 - 10.1137/S0040585X9798124X
DO - 10.1137/S0040585X9798124X
M3 - Article
AN - SCOPUS:27144433814
VL - 49
SP - 531
EP - 540
JO - Theory of Probability and its Applications
JF - Theory of Probability and its Applications
SN - 0040-585X
IS - 3
ER -
ID: 75022218