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Fully nonlinear stochastic and rough PDE...

Buckdahn, Rainer...

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Fully nonlinear stochastic and rough PDEs: Classical and viscosity solutions by Buckdahn, Rainer ( Author )

Content Provider	Lemonjar Open Access
Publisher	Australian National University
Publication Date	07-09-2023
Summary	We study fully nonlinear second-order (forward) stochastic partial differential equations (SPDEs). They can also be viewed as forward path-dependent PDEs (PPDEs) and will be treated as rough PDEs (RPDEs) under a unified framework. We develop first a local theory of classical solutions and define then viscosity solutions through smooth test functions. Our notion of viscosity solutions is equivalent to the alternative one using semi-jets. Next, we prove basic properties such as consistency, stability, and a partial comparison principle in the general setting. When the diffusion coefficient is semi-linear (but the drift can be fully nonlinear), we establish a complete theory, including global existence and comparison principle. Our methodology relies heavily on the method of characteristics.
ISBN	-
Item Type	Article
File Type	pdf
File Size	29.34 KB
Language	English
Subjects	-
Unlimited	MYR 0.01
Total read	-
URL	http://arxiv.org/abs/1501.06978

Citation

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AMA 11th EditionReferences

Buckdahn, Rainer. Fully nonlinear stochastic and rough PDEs: Classical and viscosity solutions. Australian National University. September 07, 2023. Accessed September 20, 2024. https://online.provdatabase.com/cite/24300

APA 7th EditionReferences

Buckdahn, Rainer. (2023). Fully nonlinear stochastic and rough PDEs: Classical and viscosity solutions. Australian National University. https://online.provdatabase.com/cite/24300

Chicago 17th EditionReferences

Buckdahn, Rainer. Fully nonlinear stochastic and rough PDEs: Classical and viscosity solutions. Australian National University. 2023. https://online.provdatabase.com/cite/24300

HarvardReferences

Buckdahn, Rainer. (2023). Fully nonlinear stochastic and rough PDEs: Classical and viscosity solutions. [Online]. Australian National University. Available from: https://online.provdatabase.com/cite/24300. (Accessed 20 September 2024).

Harvard AustraliaReferences

Buckdahn, Rainer, 2023, Fully nonlinear stochastic and rough PDEs: Classical and viscosity solutions, Australian National University, viewed 20 September 2024, <https://online.provdatabase.com/cite/24300>

MLA 9th EditionWorks Cited

Buckdahn, Rainer. Fully nonlinear stochastic and rough PDEs: Classical and viscosity solutions. Australian National University, 2023. PROV Database, https://online.provdatabase.com/cite/24300.

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