Richard F. Bass

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We investigate when a trigonometric polynomial p of degree M in d variables is uniquely determined by its sampled values p(x j) on a random set of points x j in the unit cube (the " sampling problem for trigonometric polynomi-als ") and estimate the probability distribution of the condition number for the associated Vandermonde-type and Toeplitz-like(More)
This paper is a survey of uniqueness results for stochastic differential equations with jumps and regularity results for the corresponding harmonic functions. 1 1. Introduction. Researchers have increasingly been studying models from economics and from the natural sciences where the underlying randomness contains jumps. To give an example from financial(More)
We investigate the relationships between the parabolic Harnack inequality, heat kernel estimates, some geometric conditions, and some analytic conditions for random walks with long range jumps. Unlike the case of diffusion processes, the parabolic Harnack inequality does not, in general, imply the corresponding heat kernel estimates.