Application of boundary functionals of random processes in statistical physics

What is it about?

In statistical physics and in numerous applications, as well as in chemistry, biology, economics and other disciplines, the concept of the first-passage time of the first reaching of a certain level or lifetime by a random process is widely and effectively used. The time of the first-passage time is only one of many boundary functionals of random processes. In this article, a number of other boundary functionals (the value of the process at the moment of reaching the level, the moment of reaching extreme values, the time the process stays above a fixed level, and other functionals, are considered for the description of physical, chemical, and biological problems) and several examples of their application in various problems are considered.

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Photo by Dmytro Dovgan on Unsplash

Photo by Dmytro Dovgan on Unsplash

Why is it important?

The first-passage time boundary functional has proven to be very effective in investigating a wide variety of problems. Perhaps other boundary functionals will be equally useful and effective.