Hitting time of a moving boundary for a diffusion

R. F. Bass and K. B. Erickson

Stochastic Processes and their Applications, 1983, vol. 14, issue 3, 315-325

Abstract: We obtain asymptotic estimates for the quantity r = log P[Tf[rang]t] as t --> [infinity] where Tf = inf\s{s : X(s)[rang]f(s)\s} and X is a real diffusion in natural scale with generator a(x) d2(·)/dx2 and the 'boundary' f(s) is an increasing function. We impose regular variation on a and f and the result is expressed as r = [integral operator]t0 [lambda]1 (f(s) ds(1 + o(1)) where [lambda]1(f) is the smallest eigenvalue for the process killed at ±f.

Keywords: Diffusion; regular; variation; eigenvalue; moving; boundary (search for similar items in EconPapers)
Date: 1983
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