Ito versus Stratonovich revisited
نویسندگان
چکیده
It is shown that a digital simulation of a noise induced phase transition using an algorithm consistent with the Ito stochastic calculus is in agreement with the predictions of that theory, whereas experiments with an analogue simulator yield measured results in agreement with the predictions of the Stratonovich theory.
منابع مشابه
On the interpretation of Stratonovich calculus
The Itô–Stratonovich dilemma is revisited from the perspective of the interpretation of Stratonovich calculus using shot noise. Over the long time scales of the displacement of an observable, the principal issue is how to deal with finite/ zero autocorrelation of the stochastic noise. The former (non-zero) noise autocorrelation structure preserves the normal chain rule using a mid-point selecti...
متن کاملOn the Relation of Anticipative Stratonovich and Symetric Integrals: a Decomposition Formula
o m=l 0 where o denotes generalized Stratonovich integration and the equality is a.s. (cf. lemma 4). We use the criteria we derive to provide some new relations between Stratonovich and Ogawa integrals which do not go through an intermediate chaos decomposition as in [1]. The results below are an outgrowth of some extensions of the Ito lemma pointed out in [2], especially lemma (4.2) there. We ...
متن کاملThe Effects of Different SDE Calculus on Dynamics of Nano-Aerosols Motion in Two Phase Flow Systems
Langevin equation for a nano-particle suspended in a laminar fluid flow was analytically studied. The Brownian motion generated from molecular bombardment was taken as a Wiener stochastic process and approximated by a Gaussian white noise. Euler-Maruyama method was used to solve the Langevin equation numerically. The accuracy of Brownian simulation was checked by performing a series of simulati...
متن کاملFokker - Planck equation with variable diffusion coefficient in the Stratonovich approach
We consider the Langevin equation with multiplicative noise term which depends on time and space. The corresponding Fokker-Planck equation in Stratonovich approach is investigated. Its formal solution is obtained for an arbitrary multiplicative noise term given by g(x, t) = D(x)T (t), and the behaviors of probability distributions, for some specific functions of D(x), are analyzed. In particula...
متن کاملStochastic Calculus in Physics
The relationship of the Ito-Stratonovich stochastic calculus to studies of weakly colored noise is explained. A functional calculus approach is used to obtain an effective Fokker-Planck equation for the weakly colored noise regime. In a smooth limit, this representation produces the Stratonovich version of the ItoStratonovich calculus for white noise. It also provides an approach to steady stat...
متن کامل