User:Iqbalhamada

In problems of stochastic analysis and in the investigation of certain physical problems -in particular, in hydromechanics-, it is necessary to construct a field, i.e., two-parameter random functions with stationary increments. Fractional Brownian fields may serve as an example of such functions. To consider, stochastic differential equations with fractional Brownian fields, it is necessary to construct first a theory of integration with respect to those fields, witch is done in the present thesis. The main objective of this thesis is to study the so-called Equations Differentials Stochastics Involving Two-parameter Fractional Brownian Motion. This thesis consist of three chapters, Element of Fractional Brownian Motion, Stochastic Integration with Respect to Two-parameter Fractional Brownian Motion, Existence and Uniqueness of the Solutions of SDE with Two- Parameter Fractional Brownian Motion. The first chapter is divide in two section, in the first we give the definition of Fractional Brownian Motion (case of one parameter), and some properties; in the second section we give the necessary notion of Two-parameter Fractional Brownian Motion and Hölder properties of Two-parameter Fractional Brownian Motion. In the second chapter we study in the first section Pathwise Integration in Two-parameter Besov Spaces of Two-parameter Fractional Brownian Motion, the second section is auxiliary we give some additional properties of Two-parameter Fractional Brownian Motion, in this section we do not present the proofs of auxiliary properties, we refer to see [9] for more detail. The Existence and Uniqueness of the Solutions of SDE with Two-Parameter Fractional Brownian Motion are given in last chapter.