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Intrinsic Stochastic Differential Equations as jets

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Intrinsic Stochastic Differential Equations as jets. / Armstrong, John; Brigo, Damiano.

In: Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences, Vol. 474, No. 2210, 28.02.2018, p. 1-28.

Research output: Contribution to journalArticlepeer-review

Harvard

Armstrong, J & Brigo, D 2018, 'Intrinsic Stochastic Differential Equations as jets', Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences, vol. 474, no. 2210, pp. 1-28. https://doi.org/10.1098/rspa.2017.0559

APA

Armstrong, J., & Brigo, D. (2018). Intrinsic Stochastic Differential Equations as jets. Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences, 474(2210), 1-28. https://doi.org/10.1098/rspa.2017.0559

Vancouver

Armstrong J, Brigo D. Intrinsic Stochastic Differential Equations as jets. Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences. 2018 Feb 28;474(2210):1-28. https://doi.org/10.1098/rspa.2017.0559

Author

Armstrong, John ; Brigo, Damiano. / Intrinsic Stochastic Differential Equations as jets. In: Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences. 2018 ; Vol. 474, No. 2210. pp. 1-28.

Bibtex Download

@article{a80389f0743f4e54a9d5c9fbdbd7e74d,
title = "Intrinsic Stochastic Differential Equations as jets",
abstract = "We explain how Ito 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 show how jets can be used to derive graphical representations of Ito SDEs. We show how jetscan be used to derive the differential operators associated with SDEsin a coordinate free manner. We relate jets to vector flows, giving ageometric interpretation of the Ito-Stratonovich transformation. We show how percentiles can be used to give an alternativecoordinate 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 particularthe median of a SDE solution is associated to the drift of the SDE in Stratonovich form for small times.",
author = "John Armstrong and Damiano Brigo",
year = "2018",
month = feb,
day = "28",
doi = "10.1098/rspa.2017.0559",
language = "English",
volume = "474",
pages = "1--28",
journal = "Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences",
issn = "1364-5021",
publisher = "Royal Society of London",
number = "2210",

}

RIS (suitable for import to EndNote) Download

TY - JOUR

T1 - Intrinsic Stochastic Differential Equations as jets

AU - Armstrong, John

AU - Brigo, Damiano

PY - 2018/2/28

Y1 - 2018/2/28

N2 - We explain how Ito 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 show how jets can be used to derive graphical representations of Ito SDEs. We show how jetscan be used to derive the differential operators associated with SDEsin a coordinate free manner. We relate jets to vector flows, giving ageometric interpretation of the Ito-Stratonovich transformation. We show how percentiles can be used to give an alternativecoordinate 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 particularthe median of a SDE solution is associated to the drift of the SDE in Stratonovich form for small times.

AB - We explain how Ito 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 show how jets can be used to derive graphical representations of Ito SDEs. We show how jetscan be used to derive the differential operators associated with SDEsin a coordinate free manner. We relate jets to vector flows, giving ageometric interpretation of the Ito-Stratonovich transformation. We show how percentiles can be used to give an alternativecoordinate 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 particularthe median of a SDE solution is associated to the drift of the SDE in Stratonovich form for small times.

U2 - 10.1098/rspa.2017.0559

DO - 10.1098/rspa.2017.0559

M3 - Article

VL - 474

SP - 1

EP - 28

JO - Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences

JF - Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences

SN - 1364-5021

IS - 2210

ER -

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