TY - CPAPER
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 - http://dx.doi.org/10.1007/978-3-319-68445-1
UR - http://hdl.handle.net/10044/1/52412
ER -