Conditioning a diffusion at first-passage and last-exit times, and a mirage arising in drug therapy for HIV

DOI10.1016/0025-5564(93)90061-EzbMath0783.92018OpenAlexW2050118410WikidataQ52394294 ScholiaQ52394294MaRDI QIDQ1261975

Simeon M. Berman

Publication date: 7 September 1993

Published in: Mathematical Biosciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0025-5564(93)90061-e

zbMATH Keywords

Ornstein-Uhlenbeck processhomogeneous diffusionfirst-passage timedrug therapyAZT treatmentBrownian motion with constant driftimmune system of HIV-positive individualslast- exit timenonhomogeneous diffusionreal-valued diffusion process

Mathematics Subject Classification ID

Medical applications (general) (92C50) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70)

Cites Work

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• The Brownian escape process
• Martingales and One-Dimensional Diffusion
• A stochastic model for the distribution of HIV latency time based on T4 counts
• A decomposition of Bessel Bridges
• Time Reversions of Markov Processes
• Times to intermittent and to permanent failures as Brownian crossing times
• Continuity Properties of Sample Functions of Markov Processes

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