Abstract
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.
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.
| Original language | English |
|---|---|
| Title of host publication | Geometric Science of Information - 3rd International Conference, GSI 2017, Proceedings |
| Publisher | Springer Verlag |
| Pages | 543-551 |
| Number of pages | 9 |
| Volume | 10589 LNCS |
| ISBN (Electronic) | 978-3-319-68445-1 |
| ISBN (Print) | 9783319684444 |
| DOIs | |
| Publication status | E-pub ahead of print - 24 Oct 2017 |
| Event | 3rd International Conference on Geometric Science of Information, GSI 2017 - Paris, France Duration: 7 Nov 2017 → 9 Nov 2017 |
Publication series
| Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
|---|---|
| Volume | 10589 LNCS |
| ISSN (Print) | 03029743 |
| ISSN (Electronic) | 16113349 |
Conference
| Conference | 3rd International Conference on Geometric Science of Information, GSI 2017 |
|---|---|
| Country/Territory | France |
| City | Paris |
| Period | 7/11/2017 → 9/11/2017 |