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DY: Dynamik und Statistische Physik

DY 51: Einstein Symposium Brownian Motion, Diffusion and Beyond (SYBM) – Contributed Talks II

DY 51.6: Talk

Wednesday, March 9, 2005, 11:30–11:45, TU H2032

Oscillating first passage time densities of strongly non-Markovian random processes. — •Tatiana Verechtchaguina, Igor M. Sokolov, and Lutz Schimansky-Geier — Institute for Physics, Humboldt University of Berlin, Newton Str. 15, 12489 Berlin

The first passage time (FPT) densities in many noise-driven dynamical systems do not resemble monomodal distribution with an exponential tail typical for Markovian systems. An example are interspike interval densities in resonant neurons driven by intrinsic noise and (or) external signal. The problem of finding ISI density can be reformulated as the first passage time problem for a non-Markovian random process with reset to a prescribed initial state after crossing a fixed barrier value.

As a mathematical example we consider a strongly underdamped harmonic oscillator driven with white Gaussian or colored harmonic noise. Using the general expression for the FPT density through multiple level-crossing densities of a stationary random process and truncating the corresponding integral series one obtains a good approximation for short and intermediate times which works especially well for processes with narrow spectral density, i.e. when the Markovian approaches fail, and reproduces very well quite a few first peaks of FPT densities.