Presentations at 39th Lithuanian national physics conference
We have contributed two presentations towards the recent 39th Lithuanian National Physics Conference, which was organized by Vilnius University and Lithuanian Physicist Society. Oral presentation by A. Kononovicius was based on some of the models presented on Physics of Risk website, while poster presentation by R. Kazakevičius tackles very general problem related to the Physics of Risk.
Oral presentation Microscopic justification of stochastic models (authors: A. Kononovicius, V. Gontis) was based on some of the already presented models:
- Kirman’s ant colony model,
- Unidirectional Kirman’s model,
- Agent based herding model of financial markets.
While description of another model, related to the multifractality of time series, will be published on Physics of Risk in the near time.
Poster presentation Study of Gaussianity of 1/f fluctuations (authors: R. Kazakevičius, B. Kaulakys) has considered a problem of obtaining pink noise, \( S(f) \sim 1/f \), from Gaussian signal. Usually it is thought that pink noise is related to the power law distributions, but apprantely it is possible to obtain pink noise from Gaussian signal. This is shown by numerically solving set of Langevin equations:
\begin{equation} \mathrm{d} I = - \gamma(t) I \mathrm{d} t + \sigma_0\gamma(t)^{\mu} \mathrm{d} W_I , \end{equation}
\begin{equation} \mathrm{d} \gamma = \sigma_\gamma\gamma^{-\frac{\eta}{2}} \mathrm{d} W_\gamma . \end{equation}
It shouldn't be hard to show that if \( \mu = 0.5 \) values of I follow normal distribution, while in the opposite case distribution of I has power law, \( \lambda = \frac{3+2(\eta-\mu)}{1 - 2 \mu} \), dependent region. It is also known that spectral density of I also has a power law, \( \beta = 1 - (\eta + 2 \mu) \), dependent region.
