Fractional noise destroys or induces a stochastic bifurcation

Chaos. 2013 Dec;23(4):043120. doi: 10.1063/1.4830271.


Little seems to be known about the stochastic bifurcation phenomena of non-Markovian systems. Our intention in this paper is to understand such complex dynamics by a simple system, namely, the Black-Scholes model driven by a mixed fractional Brownian motion. The most interesting finding is that the multiplicative fractional noise not only destroys but also induces a stochastic bifurcation under some suitable conditions. So it opens a possible way to explore the theory of stochastic bifurcation in the non-Markovian framework.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Models, Theoretical*
  • Signal-To-Noise Ratio
  • Stochastic Processes