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Articles 1 - 3 of 3
Full-Text Articles in Probability
Review Of: Charles R. Bennett, Risks In The Environment: How To Assess Them, Penny Dean
Review Of: Charles R. Bennett, Risks In The Environment: How To Assess Them, Penny Dean
RISK: Health, Safety & Environment (1990-2002)
Review of: Charles R. Bennett, Risks in the Environment: How to Assess Them (Burloak Publications 1996). Appendices, references for the appendices, prologue. ISBN 0-9680438-0-1 [305 pp. Paper $23.95. 277 Belvenia Rd., Burlington, Ontario.]
Spatial Estimates For Stochastic Flows In Euclidean Space, Salah-Eldin A. Mohammed, Michael K. R. Scheutzow
Spatial Estimates For Stochastic Flows In Euclidean Space, Salah-Eldin A. Mohammed, Michael K. R. Scheutzow
Articles and Preprints
We study the behavior for large |x| of Kunita-type stochastic flows φ(t, ω, x) on Rd, driven by continuous spatial semimartingales. For this class of flows we prove new spatial estimates for large |x|, under very mild regularity conditions on the driving semimartingale random field. It is expected that the results would be of interest for the theory of stochastic flows on noncompact manifolds as well as in the study of nonlinear filtering, stochastic functional and partial differential equations. Some examples and counterexamples are given.
Convergence Of Random Walks On The Circle Generated By An Irrational Rotation, Francis E. Su
Convergence Of Random Walks On The Circle Generated By An Irrational Rotation, Francis E. Su
All HMC Faculty Publications and Research
Fix . Consider the random walk on the circle which proceeds by repeatedly rotating points forward or backward, with probability , by an angle . This paper analyzes the rate of convergence of this walk to the uniform distribution under ``discrepancy'' distance. The rate depends on the continued fraction properties of the number . We obtain bounds for rates when is any irrational, and a sharp rate when is a quadratic irrational. In that case the discrepancy falls as (up to constant factors), where is the number of steps in the walk. This is the first example of a sharp …