He joined the faculty of Rutgers University from 1968 to 1974. In 1974 he joined Purdue University where he served as a professor of Statistics and Mathematics until achieving emeritus status in 2014.[3]
Davis's research focuses on the interconnections between classical analysis (particularly harmonic analysis), probability theory, and stochastic processes. His most notable contributions include:
Brownian motion and potential theory: He explored the relationship between Brownian motion and concepts from complex analysis and potential theory, including the work on the moments of the lifetime and conditioned Brownian motion in various domains.[5]
Random walks: Davis has published research on reinforced random walks, a class of self-interacting random processes where the probability of a step is proportional to the time already spent at the neighboring vertex.[6]
He has supervised at least seven doctoral students.[2]
Awards and honors
Davis was named a Top Ten Outstanding Teacher in the College of Science in 1999.[1]
He was elected a Fellow of the Institute of Mathematical Statistics, a distinction recognizing individuals who have made "outstanding contributions to the development and application of statistics and probability."[7]
Selected publications
Davis has published over 50 peer-reviewed articles in major mathematical and statistical journals.[1] Among them are:
Davis, B. (1976). On the norms of stochastic integrals and other martingales. Duke Mathematical Journal, 43(4), 697–704.[1]
Davis, B. (1979). Brownian motion and analytic functions. Annals of Probability, 7(6), 913–932.[1]
Davis, B., & Volkov, S. (2004). Vertex reinforced random jump processes on trees and finite graphs. Probability Theory and Related Fields, 128(1), 42–62.[5]
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