  In this paper, we introduce two new matrix stochastic processes: fractional
Wishart processes and $\varepsilon$-fractional Wishart processes with integer
indices which are based on the fractional Brownian motions and then extend
$\varepsilon$-fractional Wishart processes to the case with non-integer
indices. Both of two kinds of processes include classic Wishart processes when
the Hurst index $H$ equals $\frac{1}{2}$ and present serial correlation of
stochastic processes. Applying $\varepsilon$-fractional Wishart processes to
financial volatility theory, the financial models account for the stochastic
volatilities of the assets and for the stochastic correlations not only between
the underlying assets' returns but also between their volatilities and for
stochastic serial correlation of the relevant assets.
