Bayesian inference of fractional brownian motion of multivariate stochastic differential equations

There have been much interest in analysis of stochastic differential equation with long memory, represented by fractional diffusion process, this property have been proved itself in financial mathematic as intrinsic character of financial time series, so finding an appropriate method for estimate and analyze stochastic differential equations with long memory is a very important contemporary topic, in this paper we suggest a method for a system of stochastic differential equations with long memory, also we use the Bayesian methodology to incorporate the advanced knowledge , in addition we apply renormalized integral known in literature as Wick-It^{o}-Skorohod to solve problem of arbitrage in stochastic models (which yield inefficient mathematical stochastic models for financial market), some of conventional methods like quasi maximum likelihood , Separable Integral-Matching for Ordinary Differential Equations, and multivariate Brownian method are used to be compared with the suggested method. The suggested method has been proved to be very accurate. The estimated model used to calculate the portfolio of assets quantities allocation.