Abstract: In this paper,we obtain the integral representationof the solutionof initial value problem for stochastic Benjamin-Ono equation with gradient coupled noise, and give its application to the distribution of the biological population in estuarial areas, and then obtain distribution representation of 1-space.

Key words: initial value problem, estuarial areas, biological distribution, stochastic Benjamin-Ono equation, initial value problem, estuarial areas, biological distribution