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作者：Stong, R
摘要：This paper gives sharp bounds on the eigenvalues of a natural random walk on the group of upper triangular n x n matrices over the field of characteristic p, an odd prime, with 1's on the diagonal. In particular, this includes the finite Heisenberg groups as a special case. As a consequence we get bounds on the time required to achieve randomness for these walks. Some of the steps are done using the geometric bounds on the eigenvalues of Diaconis and Stroock. However, the crucial step is done ...
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作者：Newman, CM; Piza, MST
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作者：Bell, DR; Mohammed, SEA
作者单位：Southern Illinois University System; Southern Illinois University
摘要：We establish the existence of smooth densities for solutions of Rd-valued stochastic hereditary differential systems of the form dx(t) = H(t, x) dt + g(t, x(t - r)) dW(t). In the above equation, W is an n-dimensional Wiener process, r is a positive time delay, H is a nonanticipating functional defined on the space of paths in R(d) and g is an n X d matrix-valued function defined on [0, infinity) X R(d), such that gg* has degeneracies of polynomial order on a hypersurface in R(d). In the course...
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作者：Griffin, PS; McConnell, TR
摘要：Let T-r be the first time a sum S-n of nondegenerate i.i.d. random variables leaves a ball of radius r in some given norm on R(d). In the case of the Euclidean norm we completely characterize LP-boundedness of the overshoot parallel to S(Tr)parallel to - r in terms of the underlying distribution. For more general norms we provide a similar characterization under a smoothness condition on the norm which is shown to be very nearly sharp. One of the key steps in doing this is a characterization o...
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作者：Down, D; Meyn, SP; Tweedie, RL
作者单位：Colorado State University System; Colorado State University Fort Collins
摘要：General characterizations of geometric convergence for Markov chains in discrete time on a general state space have been developed recently in considerable detail. Here we develop a similar theory for phi-irreducible continuous time processes and consider the following types of criteria for geometric convergence: 1. the existence of exponentially bounded hitting times on one and then all suitably ''small'' sets; 2. the existence of ''Foster-Lyapunov'' or ''drift'' conditions for any one and th...
