Showing papers on "Subordinator published in 1988"
TL;DR: In this paper, it was shown that there exists a function β(t) such that ==================περγεραπεγεγαπαγε απε β(τ) = 1 a.s under certain conditions on at, and iterated logarithm results for mint(X(t+a1)-X( t)>d) as d→∞ are discussed.
6 citations
TL;DR: In this paper, a theory of linked regenerative phenomena was developed for semiregenerative sets and Markov renewal processes, and the correspondence between semireGenerative sets with Markov subordinators with a unit drift was explored.
Abstract: We develop a theory of semiregenerative phenomena. These may be viewed as a family of linked regenerative phenomena, for which Kingman [6], [7] developed a theory within the framework of quasi-Markov chains. We use a different approach and explore the correspondence between semiregenerative sets and the range of a Markov subordinator with a unit drift (or a Markov renewal process in the discrete-time case). We use techniques based on results from Markov renewal theory. SEMIREGENERATIVE PHENOMENA AND SETS; LINKED REGENERATIVE PHENOMENA: QUASI-MARKOV CHAINS; STANDARD PHENOMENA; STABLE STATES; LIFETIME; MARKOV RENEWAL PROCESSES; MARKOV ADDITIVE PROCESSES
3 citations
TL;DR: In this paper, a functional form for the lower Lipschitz condition for completely asymmetric stable processes with characteristic exponent less than one has been proved, and the functional form has been shown to be equivalent to the one in the present paper.
Abstract: Consider a completely asymmetric stable process with characteristic exponent less than one. J. Hawkes (1971, Z. Wahrscheinlichkeitstheor. Verw. Geb.17, 23–32) proved a result for the lower Lipschitz condition. In the present paper a functional form for this result is proved.