The intrinsic "sense" of stochastic differential equations

Abstract

A free choice of the integration sense would lead to the paradox that the number of possible equations (thus of solutions for a given model) can vary under a mere change of the variables. This is shown by a specific change which neutralizes the sense (by establishing a constant coupling with the noise). Its inverse singles out the Stratonovich sense, by means of the Ito formula.

Version with minor extensions

References in corpus (1)

• Stochastic differential equations: loss of the Markov property by multiplicative noise

Cited by in corpus (2)

• Stochastic differential equations: loss of the Markov property by multiplicative noise
• A maximum principle for the stochastic differential equations with multiplicative noise