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Intrinsic stochastic differential equations as jets
File | Description | Size | Format | |
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![]() | Accepted version | 14.84 MB | Adobe PDF | View/Open |
Title: | Intrinsic stochastic differential equations as jets |
Authors: | Armstrong, J Brigo, D |
Item Type: | Journal Article |
Abstract: | We explain how Itô stochastic differential equations (SDEs) on manifolds may be defined using 2-jets of smooth functions. We show how this relationship can be interpreted in terms of a convergent numerical scheme. We also show how jets can be used to derive graphical representations of Itô SDEs, and we show how jets can be used to derive the differential operators associated with SDEs in a coordinatefree manner. We relate jets to vector flows, giving a geometric interpretation of the Itô–Stratonovich transformation. We show how percentiles can be used to give an alternative coordinate-free interpretation of the coefficients of one-dimensional SDEs. We relate this to the jet approach. This allows us to interpret the coefficients of SDEs in terms of ‘fan diagrams’. In particular, the median of an SDE solution is associated with the drift of the SDE in Stratonovich form for small times. |
Issue Date: | 28-Feb-2018 |
Date of Acceptance: | 17-Jan-2018 |
URI: | http://hdl.handle.net/10044/1/57251 |
DOI: | 10.1098/rspa.2017.0559 |
ISSN: | 1364-5021 |
Publisher: | Royal Society, The |
Journal / Book Title: | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |
Volume: | 474 |
Issue: | 2210 |
Copyright Statement: | © 2018 The Author(s) Published by the Royal Society. All rights reserved. |
Keywords: | Science & Technology Multidisciplinary Sciences Science & Technology - Other Topics stochastic differential equations stochastic differential geometry stochastic differential equations on manifolds Ito calculus Stratonovich calculus jet bundle MANIFOLD 01 Mathematical Sciences 02 Physical Sciences 09 Engineering |
Notes: | The journal requires that access to the full text must be embargoed for 12 months from publication. This means that the full text version can be made available in March 2019. |
Publication Status: | Published |
Article Number: | 20170559 |
Online Publication Date: | 2018-02-14 |
Appears in Collections: | Financial Mathematics Mathematics Faculty of Natural Sciences |