Celebratio Mathematica — Rosenblatt

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Works connected to Joseph Lawson Hodges, Jr.

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J. L. Hodges, Jr. and M. Rosenblatt: “Recurrence-time moments in random walks,” Pac. J. Math. 3 : 1 (1953), pp. 127–136. MR 54190 Zbl 0050.35402 article

Consider an irreducible time-homogeneous Markov chain with discrete time. The recurrence-time moments of the states of such stochastic processes are studied. We point out that if the recurrence time of one state has its first \( k \) moments finite, then the recurrence times of all the other states have their first \( k \) moments finite. We then specialize and investigate the recurrence time moments of random walks. The main result of the paper consists of exhibiting random walks whose first \( k-1 \) recurrence-time moments exist and whose higher moments are infinite, for \( k = 1 \), \( 2,\dots \). A comparison theorem is derived that permits the moment properties of recurrence times of a large class of random walks to be determined.

K. A. Brownlee, J. L. Hodges, Jr., and M. Rosenblatt: “The up-and-down method with small samples,” J. Am. Stat. Assoc. 48 : 262 (1953), pp. 262–277. MR 55644 Zbl 0050.36002 article

Kenneth Alexander Brownlee	Related
Joseph Lawson Hodges, Jr.	Related