## Solutions to Stochastic Boundary Value Problems in Sobolev Spaces with Its Implications in Time-varying Investments

B. O. Osu *

Department of Mathematics, Abia State University, Uturu, Abia State, Nigeria.

Isaac D. D. Essi

Department of Mathematics, Rivers State University, Nkpolu Oroworokwo, Port Harcourt, Nigeria.

I. U. Amadi

Department of Mathematics and Statistics, Captain Elechi Amadi Polytechnic, Rumuola, Port Harcourt, Nigeria.

I. Davies

Department of Mathematics, Rivers State University, Nkpolu Oroworokwo, Port Harcourt, Nigeria.

*Author to whom correspondence should be addressed.

### Abstract

This paper, studied the effect of Stochastic Boundary Value Problem (SBVP) in Sobolev spaces which transited to weak formulations. The analytical solutions: the definitions, existence, uniqueness and other estimates were also obtained in weak form. The regularity conditions of the problem were considered. To establish its implications in time varying investments on one of the weak solutions; we introduced the concepts of return rates effect series to realistically assess the value of assets and its return rates for capital market. The computational and graphical results of stock variables and the effect of relevant parameters are well discussed in this paper.

Keywords: Weak solutions, SBVP, Sobolev spaces, asset prices, rate of returns

**How to Cite**

*Asian Journal of Pure and Applied Mathematics*,

*4*(1), 716–734. Retrieved from https://globalpresshub.com/index.php/AJPAM/article/view/1692

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