Our recent articles on agent-based reasoning and the burst statistics
In the next Physica A issue (will be made available in February, 2012) our article [1] will be published. The article is on the agent-based reasoning for the stochastic models. Basically this article incorporates knowledge obtained while working on the simple models provided on Physics of Risk:
- Stochastic ant colony model,
- Agent based herding model of financial markets,
- Multifractality of time series.
You can freely read a draft version in the arxiv. Or if you have access to sciencedirect.com you'll find the final version there. Note that you can freely play with the demonstrations related to the article here on the Physics of Risk.
Recently we have submitted another paper [2] related to the bursting statistics in stochastic models. In this paper we show that our model using variable transformation can be reduced to the well known Bessel process. Thus we can use the hitting times of Bessel process to analytically analyze burst statistics of our model - in the paper we analytical derive PDF for burst durations.
References
- A. Kononovicius, V. Gontis. Agent based reasoning for the non-linear stochastic models of long-range memory. Physica A 391: 1309-1314 (2012). doi: 10.1016/j.physa.2011.08.061. arXiv: 1106.2685 [q-fin.ST].
- V. Gontis, A. Kononovicius, S. Reimann. The class of nonlinear stochastic models as a background for the bursty behavior in financial markets. Advances in Complex Systems 15: 1250071 (2012). doi: 10.1142/S0219525912500713. arXiv: 1201.3083 [q-fin.ST].
