Asymptotic behavior of the sample mean of a function of the Wiener process and the MacDonald function
Vol. 16 (2009), No. 1, Page 55--93.
Albeverio, Sergio ; Fatalov, Vadim; Piterbarg, Vladimir I.
Asymptotic behavior of the sample mean of a function of the Wiener process and the MacDonald function
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]
Abstract:
Explicit asymptotic formulas for large time of expectations or distribution functions of exponential functionals of Brownian motion in terms of MacDonald's function are proven.
Keywords: Asymptotic behaviors, Sample mean, Wiener process, MacDonald function, sojourn times, Laplace method, Large deviation principle, Dirichlet forms, Schr\"{o}dinger operators, spectrum, exponential potential.
Mathematics Subject Classification (2000): Primary 60J65, secondary 60J55}
Mathematical Reviews Number: MR2548933
Received: 2008-11-11
