Partial and full solutions of stochastic differential equations

2014/05/13 by Dietrich Ryter, Ryter, Dietrich
Economics, Econometrics and Finance · #60H10 #FOS: Physical sciences #Mathematical Physics (math-ph) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1405.3066

openalex publication_date 2014/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Only the "anti-Ito" integral yields the correct shift of the mean, by the fact that the elements of its Riemannian sum hold in the order O(dt) rather than only in O(sqrt dt). The corresponding "full" Fokker-Planck equation is particularly simple and the only one applying for Brownian motion with an arbitrary friction law. The "full" backward equation coincides with it in the noise contribution.

Related

• The unique solution of stochastic differential equations with independent coefficients
• Correction of the Fokker-Planck equation, and the adequate sense of stochastic integration
• Stochastic differential equations with covariant probabilities
• The unique solution of stochastic differential equations
• The intrinsic "sense" of stochastic differential equations