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Open AccessArticle

Probabilistic Interpretation of Solutions of Linear Ultraparabolic Equations

Department of Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, NV 89154-4020, USA
Mathematics 2018, 6(12), 286; https://doi.org/10.3390/math6120286
Received: 1 November 2018 / Revised: 21 November 2018 / Accepted: 21 November 2018 / Published: 27 November 2018
(This article belongs to the Special Issue Advanced Mathematical Methods: Theory and Applications)
We demonstrate the existence, uniqueness and Galerkin approximatation of linear ultraparabolic terminal value/infinite-horizon problems on unbounded spatial domains. Furthermore, we provide a probabilistic interpretation of the solution in terms of the expectation of an associated ultradiffusion process. View Full-Text
Keywords: ultraparabolic equation; ultradiffusion process; probabilistic representation; mathematical finance ultraparabolic equation; ultradiffusion process; probabilistic representation; mathematical finance
MDPI and ACS Style

Marcozzi, M.D. Probabilistic Interpretation of Solutions of Linear Ultraparabolic Equations. Mathematics 2018, 6, 286.

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