THE CLASS OF NONLINEAR STOCHASTIC MODELS AS A BACKGROUND FOR THE BURSTY BEHAVIOR IN FINANCIAL MARKETS

We investigate behavior of the continuous stochastic signals above some threshold, bursts, when the exponent of multiplicativity is higher than one. Earlier we have proposed a general nonlinear stochastic model applicable for the modeling of absolute return and trading activity in financial markets which can be transformed into Bessel process with known first hitting (first passage) time statistics. Using these results we derive PDF of burst duration for the proposed model. We confirm derived analytical expressions by numerical evaluation and discuss bursty behavior of return in financial markets in the framework of modeling by nonlinear SDE.