Beyond Itô versus Stratonovich

Abstract

Recently, a novel framework to handle stochastic processes has emerged from a series of studies in biology, showing situations beyond 'Itô 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.

20 pages, 1 figure

References in corpus (5)

• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Stochastic Dynamical Structure (SDS) of Nonequilibrium Processes in the Absence of Detailed Balance. IV: Emerging of Stochastic Dynamical Equalities and Steady State Thermodynamics from Darwinian Dynamics
• Calculating Biological Behaviors of Epigenetic States in Phage lambda Life Cycle
• A non-equilibrium dynamic mechanism for the allosteric effect
• Stochastic equations for thermodynamics

Cited by in corpus (4)

• Marcus versus Stratonovich for Systems with Jump Noise
• Work Relations Connecting Nonequilibrium Steady States Without Detailed Balance
• Boltzmann-Gibbs entropy is sufficient but not necessary for the likelihood factorization required by Einstein
• A Stochastic Model of Inward Diffusion in Magnetospheric Plasmas