The intrinsic "sense" of stochastic differential equations

2016/05/10 by Dietrich Ryter, Ryter, Dietrich · 1 citation
Economics, Econometrics and Finance · #60H #Complex Systems and Time Series Analysis #FOS: Physical sciences #Mathematical Physics (math-ph) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1605.02897

openalex publication_date 2016/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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

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