Saddle point approximation of Rice's formula

Oskar Hagberg

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,
2005

ISSN 1403-9338

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Abstract:

The saddle point approximation of Rice's formula for the upcrossing rate of a stationary random process has until now only been informally studied. We formulate and prove a formal theorem which gives the first two terms in the saddle point expansion and slightly modify the second term.