On Some Stochastic Parabolic Systems Driven by New Fractional Brownian Motions
Mahmoud M. El-Borai *
Department of Mathematics and Computer Sciences, Faculty of Science, Alexandria University, Alexandria, Egypt.
Khairia El-Said El-Nadi
Department of Mathematics and Computer Sciences, Faculty of Science, Alexandria University, Alexandria, Egypt.
*Author to whom correspondence should be addressed.
Abstract
Vector-valued functions of new fractional Brownian motions are considered. The concept of stochastic integrals are generalized. Formulas of Ito are also generalized. Some stochastic parabolic systems driven by new fractional Brownian motions are studied. Uniqueness and existence theorems are proved. These findings have potential applications in fields such as financial mathematics, where modeling with fractional Brownian motion is relevant.
Keywords: Fractional normal distribution, riemann stochastic integrals, vectors of fractional brownian motion, ; fractional stochastic parabolic systems