Name
Abstract | ||
|---|---|---|
We explain how Ito Stochastic Differential Equations on manifolds may be defined 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 calculus for stochastic differential geometry is not necessary. We give a new geometric interpretation of the Ito-Stratonovich transformation in terms of the 2-jets of curves induced by consecutive vector flows. 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. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1007/978-3-319-68445-1_63 | GEOMETRIC SCIENCE OF INFORMATION, GSI 2017 |
DocType | Volume | ISSN |
Conference | 10589 | 0302-9743 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| John Armstrong | 1 | 0 | 1.01 |
| Damiano Brigo | 2 | 17 | 8.42 |