On the First-passage Time Problem: Cumulant Approach
نویسندگان
چکیده
The First-Passage Time (FPT) problems have numerous practical applications in fields that go from engineering and physics to finance and biology among many others. For the case of Markov gamma processes, this paper develops a methodology that combines the first Pontryagin equation approach and the cumulant analysis in order to obtain FPT statistics. For investigation about the structure of the Probability Density Function (PDF) of the FPT an orthogonal series expansion of the distribution is made and compared with an experimental version, using Stochastic Differential Equations (SDE) simulation techniques. The results show that the FPT distribution can be accurately characterized through another gamma PDF. An application of these results is also presented.
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