NONEXTENSIVE STATISTICAL MECHANICS DISTRIBUTIONS AND DYNAMICS OF FINANCIAL OBSERVABLES FROM THE NONLINEAR STOCHASTIC DIFFERENTIAL EQUATIONS

Julius Ruseckas (), Vygintas Gontis and Bronislovas Kaulakys
Additional contact information
Julius Ruseckas: Institute of Theoretical Physics and Astronomy, Vilnius University, A. Goštauto 12, LT-01108 Vilnius, Lithuania
Vygintas Gontis: Institute of Theoretical Physics and Astronomy, Vilnius University, A. Goštauto 12, LT-01108 Vilnius, Lithuania
Bronislovas Kaulakys: Institute of Theoretical Physics and Astronomy, Vilnius University, A. Goštauto 12, LT-01108 Vilnius, Lithuania

Advances in Complex Systems (ACS), 2012, vol. 15, issue supp0, 1-13

Abstract: We present nonlinear stochastic differential equations, generating processes with theq-exponential andq-Gaussian distributions of the observables, i.e. with the long-range power-law autocorrelations and1/fβpower spectral density. Similarly, the Tsallisq-distributions may be obtained in the superstatistical framework as a superposition of different local dynamics at different time intervals. In such approach, the average of the stochastic variable is generated by the nonlinear stochastic process, while the local distribution of the signal is exponential or Gaussian one, conditioned by the slow average. Further we analyze relevance of the generalized and adapted equations for modeling the financial processes. We model the inter-trade durations, the trading activity and the normalized return using the superstatistical approaches with the exponential and normal distributions of the local signals driven by the nonlinear stochastic process.

Keywords: Stochastic differential equations; Tsallis distributions; superstatistics; financial systems (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0219525912500737
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:acsxxx:v:15:y:2012:i:supp0:n:s0219525912500737

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0219525912500737

Access Statistics for this article

Advances in Complex Systems (ACS) is currently edited by Frank Schweitzer

More articles in Advances in Complex Systems (ACS) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().