The class of nonlinear stochastic models as a background for the bursty behavior in financial markets

Abstract

We investigate large changes, bursts, of the continuous stochastic signals, when the exponent of multiplicativity is higher than one. Earlier we have proposed a general nonlinear stochastic model 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 analytical expressions by numerical evaluation and discuss bursty behavior of return in financial markets in the framework of modeling by nonlinear SDE.

9 pages, 5 figures

References in corpus (5)

• A long-range memory stochastic model of the return in financial markets
• Herding model and 1/f noise
• Trading activity as driven Poisson process: comparison with empirical data
• Long-range memory model of trading activity and volatility
• Agent-based Versus Macroscopic Modeling of Competition and Business Processes in Economics

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