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Stock price change in financial market occurs through transactions in analogywith diffusion in stochastic physical systems. The analysis of price changes inreal markets shows that long-range correlations of price fluctuations largelydepend on the number of transactions. We introduce the multiplicativestochastic model of time interval between trades and analyze spectral densityand correlations of the number of transactions. The model reproduces spectralproperties of the real markets and explains the mechanism of power lawdistribution of trading activity. Our study provides an evidence thatstatistical properties of financial markets are enclosed in the statistics ofthe time interval between trades. Multiplicative stochastic diffusion may serveas a consistent model for this statistics.

Multiplicative Stochastic Model of the Time Interval between Trades in Financial Markets