On some Applications of stochastic differential equations

Abstract

Abstract In this research we have studied stochastic differential equation which came to address: On some application of stochastic differential equations. Namely Ito formula with some examples coming through theorems giving or appearing their importance for many applications in mathematics Economics, Geology and Physics. In this research we discussed in the chapter one introduction of some mathematical preliminaries (introduction) and in section one we talked about probability space, Random Variables and stochastic process also we explained some mathematical preliminaries and in section two we explained an important example (Brownian motion). In chapter two we discussed the conception of Ito integrals and in section one we talked about construction of the Ito integral, in section two we explained with some examples and in section three we explained the Ito Formula and the martingale Representation theorem and in section Four we talked about multi-dimensional Ito Formula. In chapter three which came by the title solution of stochastic differential equations there are two sections so in section one we gave examples with solution and theory of the (Existence and Uniqueness) and in section two we spoke about weak and strong solution. In chapter four we talked about Applications to Boundary value Problems, In section one we discussed that the Combined Dirichlet –Poisson problem uniqueness in section two wes explained the Generalize Dirichlet problem.