THE MALLIAVIN DERIVATIVE FOR G ENERALIZATION OF FRACTIONAL BESSEL TYPE PROCESS

Abstract

This paper considersa generalization of fractional Bessel type process. It is also a type of singular stochastic differential equations driven by fractional Brownian motion which were studied by some authors. Undersome assumptions of coefficients, this equation has a unique positive solution. The main purpose of this paper is to show the formula of the Malliavin derivative for this process.  The techniques of Malliavin calculus were applied for stochastic differential equations driven by a fractional Brownian motion. We obtain that the Malliavin derivative for this process is an exponent function of the drift coefficient's derivative.  This result is useful to estimate inverse moments of the solution. From that, we can  estimate the rate of convegence of the numerical approximation in the L_p- norm.