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BibTex format

@article{Armstrong:2018:10.1098/rspa.2017.0559,
author = {Armstrong, J and Brigo, D},
doi = {10.1098/rspa.2017.0559},
journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
title = {Intrinsic stochastic differential equations as jets},
url = {http://dx.doi.org/10.1098/rspa.2017.0559},
volume = {474},
year = {2018}
}

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TY  - JOUR
AB  - We explain how Itô stochastic differential equations(SDEs) on manifolds may be defined using 2-jets ofsmooth functions. We show how this relationship canbe interpreted in terms of a convergent numericalscheme. We also show how jets can be used toderive graphical representations of Itô SDEs, and weshow how jets can be used to derive the differentialoperators associated with SDEs in a coordinatefreemanner. We relate jets to vector flows, givinga geometric interpretation of the Itô–Stratonovichtransformation. We show how percentiles can be usedto give an alternative coordinate-free interpretation ofthe coefficients of one-dimensional SDEs. We relatethis to the jet approach. This allows us to interpretthe coefficients of SDEs in terms of ‘fan diagrams’. Inparticular, the median of an SDE solution is associatedwith the drift of the SDE in Stratonovich form for smalltimes.
AU  - Armstrong,J
AU  - Brigo,D
DO  - 10.1098/rspa.2017.0559
PY  - 2018///
SN  - 1364-5021
TI  - Intrinsic stochastic differential equations as jets
T2  - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
UR  - http://dx.doi.org/10.1098/rspa.2017.0559
UR  - http://hdl.handle.net/10044/1/57251
VL  - 474
ER  -

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