Frequency Domain Approach to Some Results on Fractional Brownian Motion

摘要

Let X be a fractional Brownian motion. It is known that M(sub t)=integral m(sub t)dX, t greater than or equal to zero, where m(sub t) is a certain kernel, denes a martingale M, and also that X can be represented by X(sub t)=integral x(sub t)dM, t greater than or equal to zero, for some kernel x(sub t). We derive these results by using the spectral representation of the covariance function of X. A formula for the covariance between X and M is also given.