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| A STRASSEN LAW OF THE ITERATED LOGARITHM FOR PROCESSES WITH INDEPENDENT INCREMENTS |
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Citation： |
Wang Jiagang.A STRASSEN LAW OF THE ITERATED LOGARITHM FOR PROCESSES WITH INDEPENDENT INCREMENTS[J].Chinese Annals of Mathematics B,1997,18(1):15~30 |
| Page view： 1039
Net amount： 761 |
Authors： |
Wang Jiagang; |
Foundation： |
The project supported by the National Natural Science
Foundation of China. |
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| Abstract： |
Let $X=\{X(t),\, t\ge 0\}$ be a process with independent increments (PII)
such that
$$
\sep[X(t)]=0,\qquad D_X(t)\deq \sep[X(t)]^2<\infty,\qquad
\lim_{t\to\infty}\frac{D_X(t)}t=1,
$$
and there exists a majoring measure $G$ for the jump $\Delta X$ of $X$. Under
these assumptions, using rather a direct method, a Strassen's law of the
iterated logarithm (Strassen LIL) is established. As some special cases,
the Strassen LIL for homogeneous PII and for partial sum process of i.i.d.
random variables are comprised. |
Keywords： |
Strassen law of the iterated logarithm,
process with independent increments, stochastic calculus |
Classification： |
60F15, 60F17, 60H05, 60G50 |
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