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Full-Text Articles in Probability
Stochastic Functional Differential Equations On Manifolds, Rémi Léandre, Salah-Eldin A. Mohammed
Stochastic Functional Differential Equations On Manifolds, Rémi Léandre, Salah-Eldin A. Mohammed
Articles and Preprints
In this paper, we study stochastic functional differential equations (sfde's) whose solutions are constrained to live on a smooth compact Riemannian manifold. We prove the existence and uniqueness of solutions to such sfde's. We consider examples of geometrical sfde's and establish the smooth dependence of the solution on finite-dimensional parameters.
Discrepancy Convergence For The Drunkard's Walk On The Sphere, Francis E. Su
Discrepancy Convergence For The Drunkard's Walk On The Sphere, Francis E. Su
All HMC Faculty Publications and Research
We analyze the drunkard's walk on the unit sphere with step size θ and show that the walk converges in order C/sin2(θ) steps in the discrepancy metric (C a constant). This is an application of techniques we develop for bounding the discrepancy of random walks on Gelfand pairs generated by bi-invariant measures. In such cases, Fourier analysis on the acting group admits tractable computations involving spherical functions. We advocate the use of discrepancy as a metric on probabilities for state spaces with isometric group actions.
A Bonanza Of Birthday Bewilderments, Dale K. Hathaway
A Bonanza Of Birthday Bewilderments, Dale K. Hathaway
Faculty Scholarship – Mathematics
The birthday problem is a popular probability conundrum at least partially because of the apparent counterintuitive result. But the results are not unexpected if the number of opportunities is considered. This article uses the opportunities approach to solve several variations of the birthday problem.