Abstract
We construct a diffusion process in the infinite-dimensional simplex consisting of all nonincreasing infinite sequences of nonnegative numbers with sum less than or equal to one. The process is constructed as a limit of a certain sequence of Markov chains. The state space of the nth chain is the set of all strict partitions of n (that is, partitions with distinct parts). As n →∞, these random walks converge to a continuous-time strong Markov process in the infinite-dimensional simplex. The process has continuous sample paths. The main result about the limit process is an expression for its pre-generator as a formal second-order differential operator in a polynomial algebra. Bibliography: 29 titles.
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