Extension of a stochastic integral with respect to cylindrical martingales

Leszek Gawarecki

doi:10.1016/S0167-7152(96)00171-X

Extension of a stochastic integral with respect to cylindrical martingales

Leszek Gawarecki

Kettering University

Research output: Contribution to journal › Article › peer-review

Abstract

We extend stochastic integral of Metivier and Pellaumail with respect to cylindrical martingales which is necessary for constructing a Hilbert space-valued diffusion based on Nelson's kinematic theory of stochastic motion. Examples for inadequacy of existing stochastic integrals are provided.

Original language	American English
Journal	Statistics Probability Letters
Volume	34
DOIs	https://doi.org/10.1016/S0167-7152(96)00171-X
State	Published - Jun 2 1997

Keywords

stochastic integral
cylindrical martingales

Disciplines

Mathematics

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10.1016/S0167-7152(96)00171-XLicense: CC BY

https://www.sciencedirect.com/science/article/pii/S016771529600171X

Cite this

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title = "Extension of a stochastic integral with respect to cylindrical martingales",

abstract = " We extend stochastic integral of Metivier and Pellaumail with respect to cylindrical martingales which is necessary for constructing a Hilbert space-valued diffusion based on Nelson's kinematic theory of stochastic motion. Examples for inadequacy of existing stochastic integrals are provided.",

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year = "1997",

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AU - Gawarecki, Leszek

PY - 1997/6/2

Y1 - 1997/6/2

N2 - We extend stochastic integral of Metivier and Pellaumail with respect to cylindrical martingales which is necessary for constructing a Hilbert space-valued diffusion based on Nelson's kinematic theory of stochastic motion. Examples for inadequacy of existing stochastic integrals are provided.

AB - We extend stochastic integral of Metivier and Pellaumail with respect to cylindrical martingales which is necessary for constructing a Hilbert space-valued diffusion based on Nelson's kinematic theory of stochastic motion. Examples for inadequacy of existing stochastic integrals are provided.

KW - stochastic integral

KW - cylindrical martingales

UR - https://digitalcommons.kettering.edu/mathematics_facultypubs/10

UR - https://www.sciencedirect.com/science/article/pii/S016771529600171X

U2 - 10.1016/S0167-7152(96)00171-X

DO - 10.1016/S0167-7152(96)00171-X

M3 - Article

VL - 34

JO - Statistics Probability Letters

JF - Statistics Probability Letters

ER -

Extension of a stochastic integral with respect to cylindrical martingales

Abstract

Keywords

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