  We propose a model of fractal point process driven by the nonlinear
stochastic differential equation. The model is adjusted to the empirical data
of trading activity in financial markets. This reproduces the probability
distribution function and power spectral density of trading activity observed
in the stock markets. We present a simple stochastic relation between the
trading activity and return, which enables us to reproduce long-range memory
statistical properties of volatility by numerical calculations based on the
proposed fractal point process.
