Hidden symmetries and equilibrium properties of multiplicative white-noise stochastic processes

作者：Gonzalez Arenas Zochil; Barci Daniel G

来源：Journal of Statistical Mechanics: Theory and Experiment , 2012, 2012(12): P12005.

DOI：10.1088/1742-5468/2012/12/P12005

• stochastic particle dynamics (theory)
• fluctuations (theory)
• stochastic processes (theory)

Multiplicative white-noise stochastic processes continue to attract attention in a wide area of scientific research. The variety of prescriptions available for defining them makes the development of general tools for their characterization difficult. In this work, we study equilibrium properties of Markovian multiplicative white-noise processes. For this, we define the time reversal transformation for such processes, taking into account that the asymptotic stationary probability distribution depends on the prescription. Representing the stochastic process in a functional Grassmann formalism, we avoid the necessity of fixing a particular prescription. In this framework, we analyze equilibrium properties and study hidden symmetries of the process. We show that, using a careful definition of the equilibrium distribution and taking into account the appropriate time reversal transformation, usual equilibrium properties are satisfied for any prescription. Finally, we present a detailed deduction of a covariant supersymmetric formulation of a multiplicative Markovian white-noise process and study some of the constraints that it imposes on correlation functions using Ward-Takahashi identities.

• 出版日期2012-12