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Level crossings and other level functionals of stationary Gaussian processes
Gaussian processes/fields Hermite polynomials level curve level functionals local time (factorial) moments
2009/5/18
This paper presents a synthesis on the mathematical work done on level crossings of stationary Gaussian processes, with some extensions. The main results [(factorial) moments, representation into the ...
The Distribution of Time Spent by a Standard Excursion Above a Given Level, with Applications to Ring Polymers near a Discontinuity in Potential
Standard Brownian Excursions Brownian Bridges Ring Polymers End-Attached Polymers
2009/5/8
The law for the time tau_{a} spent by a standard Brownian excursion above a given level a>0 is found using Ito excursion theory. This is achieved by conditioning the excursion to have exactly one mark...