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Itô stochastic differential equations as 2-jets

Research output: Chapter in Book/Report/Conference proceedingConference paper

Original languageEnglish
Title of host publicationGeometric Science of Information - 3rd International Conference, GSI 2017, Proceedings
PublisherSpringer Verlag
Number of pages9
Volume10589 LNCS
ISBN (Electronic)978-3-319-68445-1
ISBN (Print)9783319684444
Accepted/In press27 Sep 2017
E-pub ahead of print24 Oct 2017
Event3rd International Conference on Geometric Science of Information, GSI 2017 - Paris, France
Duration: 7 Nov 20179 Nov 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10589 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349


Conference3rd International Conference on Geometric Science of Information, GSI 2017


King's Authors


We explain how It^o Stochastic Dierential Equations on man-
ifolds may be dened as 2-jets of curves and show how this relationship
can be interpreted in terms of a convergent numerical scheme. We use
jets as a natural language to express geometric properties of SDEs. We
explain that the mainstream choice of Fisk-Stratonovich-McShane cal-
culus for stochastic dierential geometry is not necessary. We give a new
geometric interpretation of the It^o{Stratonovich transformation in terms
of the 2-jets of curves induced by consecutive vector
ows. We discuss the forward Kolmogorov equation and the backward diffusion operator in geometric terms. In the one-dimensional case we consider percentiles
of the solutions of the SDE and their properties. In particular the median
of a SDE solution is associated to the drift of the SDE in Stratonovich
form for small times.

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