Calculations on stopping time and return period

Establishing protective projects such as breakwaters and flood barriers is the key to preventing marine disasters caused by extreme sea conditions. One of the core technical problems in implementing these large-scale projects is how to determine the fortification criteria reasonably. In the past, research based on random variables studied the determined state of time for the stochastic process. For the first time, this paper studies the statistical characteristics of ocean environment elements from both the time and space with the real perspective of the stochastic process and introduces the concept of stopping time in stochastic processes into the analysis of storm surge. The relationship between the stopping time and threshold selection for the measured data is discussed. The relationship between the wave front displacement and the time exceeding the threshold $$\lambda$$ is given as $$\tau = \inf \left\{ {t \ge 0:\xi \left( t \right) > \lambda } \right\}$$. When the distribution is symmetrical and has Markov characteristics, there is $$P\left( {\tau \le t} \right) = 2P\left( {\xi \left( t \right) > \lambda } \right)$$. Additionally, the relationship between the calculation and the return period of the wave height is given. It is proved that the stopping time $$N = \inf \left\{ {n \ge 1:X_{n} > x_{0} } \right\}$$ obeys the geometric distribution, and the expectation of the stopping time is the return period in the ocean engineering. Through the analysis of the stopping time parameters, the rationality of applying the Gumbel distribution in extreme sea conditions for calculating return period is given. With the relationship between the service life of marine engineering and the commonly used parameters, the average life expectancy of offshore engineering is: $${\text{ET}} = 5$$.