arXiv subjects
Publications and source records attributed to Kouji Yamamuro.
Relations between subexponential densities and locally subexponential distributions are discussed. It is shown that the class of subexponential densities is neither closed under convolution roots nor closed under asymptotic equivalence. A remark is given on the closure under convolution roots for the class of convolution equivalent distributions.
Laws of the iterated logarithm of "limsup" type are studied for multi-dimensional selfsimilar processes $\{X(t)\}$ with independent increments having exponent $H$. It is proved that, for any positive increasing function $g(t)$ with $\displaystyle \lim_{t\to\infty}g(t) = \infty$, there is $C\in [0,\infty]$ such that $\limsup|X(t)|/(t^Hg(|\log t|))= C$ a.s. as $t \to\infty $, in addition, as $t \to 0$. A necessary and sufficient condition for the existence of $g(t)$ with C=1 is obtained. In the case where $g(t)$ with C=1 does not exist, a criterion to classify functions $g(t)$ according to C=0 or $C=\infty$ is given. Moreover, various "limsup" type laws with identification of the positive constants $C$ are explicitly presented in several propositions and examples. The problems that exchange the roles of $\{X(t)\}$ and $g(t)$ are also discussed.