Record statistics for biased random walks, with an application to financial data.

@article{Wergen2011RecordSF,
  title={Record statistics for biased random walks, with an application to financial data.},
  author={Gregor Wergen and Miro Bogner and Joachim H A Krug},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2011},
  volume={83 5 Pt 1},
  pages={
          051109
        }
}
  • G. WergenM. BognerJ. Krug
  • Published 4 March 2011
  • Mathematics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
We consider the occurrence of record-breaking events in random walks with asymmetric jump distributions. The statistics of records in symmetric random walks was previously analyzed by Majumdar and Ziff [Phys. Rev. Lett. 101, 050601 (2008)] and is well understood. Unlike the case of symmetric jump distributions, in the asymmetric case the statistics of records depends on the choice of the jump distribution. We compute the record rate P(n)(c), defined as the probability for the nth value to be… 

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References

SHOWING 1-10 OF 31 REFERENCES

Statistics of Persistent Events in the Binomial Random Walk: Will the Drunken Sailor Hit the Sober Man?

The statistics of persistent events, recently introduced in the context of phase ordering dynamics, is investigated in the case of the one-dimensional lattice random walk in discrete time. We

Driven particle in a random landscape: disorder correlator, avalanche distribution, and extreme value statistics of records.

The renormalized force correlator Delta(micro) can be measured directly in numerics and experiments on the dynamics of elastic manifolds in the presence of pinning disorder, and the Middleton theorem is violated.

Records and sequences of records from random variables with a linear trend

We consider records and sequences of records drawn from discrete time series of the form Xn = Yn + cn, where the Yn are independent and identically distributed random variables and c is a constant

Record-breaking temperatures reveal a warming climate

We present a mathematical analysis of records drawn from independent random variables with a drifting mean. To leading order the change in the record rate is proportional to the ratio of the drift

An Introduction to Econophysics: Correlations and Complexity in Finance

Economists and workers in the financial world will find useful the presentation of empirical analysis methods and well-formulated theoretical tools that might help describe systems composed of a huge number of interacting subsystems.

Fear and its implications for stock markets

Abstract.The value of stocks, indices and other assets, are examples of stochastic processes with unpredictable dynamics. In this paper, we discuss asymmetries in short term price movements that can

An Introduction To Probability Theory And Its Applications

A First Course in Probability (8th ed.) by S. Ross is a lively text that covers the basic ideas of probability theory including those needed in statistics.