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[size=1.2em]Journal of Statistical Mechanics: Theory and Experiment [size=1.2em]Volume 2012[size=1.2em]July 2012
[size=1.2em]Ruoshi Yuan and Ping Ao J. Stat. Mech. (2012) P07010 doi:10.1088/1742-5468/2012/07/P07010
Beyond It versus Stratonovich
[size=1.2em]Ruoshi Yuan1 and Ping Ao2
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[size=1.4em]AbstractReferencesCited By
Paper[size=1.2em]
[size=1em]Recently, a novel framework to handle stochastic processes has emerged from a series of studies in biology, showing situations beyond 'It versus Stratonovich'. Its internal consistency can be demonstrated via the zero mass limit of a generalized Klein–Kramers equation. Moreover, the connection to other integrations becomes evident: the obtained Fokker–Planck equation defines a new type of stochastic calculus that in general differs from the α-type interpretation. A unique advantage of this new approach is a natural correspondence between stochastic and deterministic dynamics, which is useful or may even be essential in practice. The core of the framework is a transformation from the usual Langevin equation to a form that contains a potential function with two additional dynamical matrices, which reveals an underlying symplectic structure. The framework has a direct physical meaning and a straightforward experimental realization. A recent experiment has offered a first empirical validation of this new stochastic integration.
Keywords
[size=1.2em]energy landscapes (theory)
[size=1.2em]systems biology
[size=1.2em]stochastic processes (theory)
[size=1.2em]brownian motion
PACS[size=1.2em]87.10.-e General theory and mathematical aspects
[size=1.2em]87.85.Lf Tissue engineering
[size=1.2em]87.23.Kg Dynamics of evolution
[size=1.2em]02.50.Ey Stochastic processes
MSC[size=1.2em]92B05 General biology and biomathematics
[size=1.2em]92D10 Genetics (For genetic algebras, see 17D92)
Subjects[size=1.2em]Computational physics
[size=1.2em]Biological physics
[size=1.2em]Environmental and Earth science
Dates[size=1.2em]Issue 07 (July 2012)
[size=1.2em]Received 2 February 2012, accepted for publication 17 June 2012
[size=1.2em]Published 16 July 2012
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[size=1.2em]Ruoshi Yuan and Ping Ao J. Stat. Mech. (2012) P07010
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