Imperial College London


Faculty of Natural SciencesDepartment of Mathematics

Chair in Mathematical Finance







805Weeks BuildingSouth Kensington Campus






BibTex format

author = {Armstrong, J and Brigo, D},
doi = {10.1007/978-3-319-68445-1},
publisher = {Springer Verlag},
title = {Ito Stochastic Differential Equations as 2-Jets},
url = {},

RIS format (EndNote, RefMan)

AB - We explain how Itˆo Stochastic Differential Equations on manifoldsmay be defined as 2-jets of curves and show how this relationshipcan be interpreted in terms of a convergent numerical scheme. We usejets as a natural language to express geometric properties of SDEs. Weexplain that the mainstream choice of Fisk-Stratonovich-McShane calculusfor stochastic differential geometry is not necessary. We give a newgeometric interpretation of the Itˆo–Stratonovich transformation in termsof the 2-jets of curves induced by consecutive vector flows. We discussthe forward Kolmogorov equation and the backward diffusion operatorin geometric terms. In the one-dimensional case we consider percentilesof the solutions of the SDE and their properties. In particular the medianof a SDE solution is associated to the drift of the SDE in Stratonovichform for small times.
AU - Armstrong,J
AU - Brigo,D
DO - 10.1007/978-3-319-68445-1
PB - Springer Verlag
SN - 0302-9743
TI - Ito Stochastic Differential Equations as 2-Jets
UR -
UR -
ER -