Tree rings in the study of future change

The various groundbased and spaceborne sensors in use today offer the possibility of detecting practically all the major kinds of corpuscular and electromagnetic radiation emanating from processes occurring on the Sun and in interplanetary and interstellar space, in real time. It would be difficult to overemphasize the importance of such studies. At the same time direct methods do not permit one to establish the characteristics of the astrophysical and geophysical processes over a large time scale. To solve these problems, which are essential for both theory and practice, one has to have eyewitnesses of the past who would be capable, as it were, not only of recording a phenomenon but of retaining the relevant information in their memory in its original form as well. Such outstanding eyewitnesses of the past are trees, which contain in their annual rings information both on the local conditions of growth and on the global properties of the Earth’s atmosphere as a whole and of interplanetary space and solar activity

A Renewal Approach to Markovian U-statistics

In this paper we describe a novel approach to the study of U-statistics in the markovian setup, based on the (pseudo-) regenerative properties of Harris Markov chains. Exploiting the fact that any sample path X1, . . . , Xn of a general Harris chain X may be divided into asymptotically i.i.d. data blocks B1, . . . , BN of ran- dom length corresponding to successive (pseudo-) regeneration times, we introduce the notion of regenerative U-statistic ΩN