Explicit solutions of the G-heat equation for a class of initial conditions

We obtain the viscosity solution of the G-heat equation with the initial condition ϕ(x)=xn for each integer n≥1 using the method of G-Brownian motion.

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Bibliographic Details
Published inNonlinear analysis Vol. 75; no. 18; pp. 6588 - 6595
Main Author Hu, Mingshang
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.12.2012
Subjects
[formula omitted]-Brownian motion
[formula omitted]-expectation
[formula omitted]-heat equation
[formula omitted]-normal distribution
Sublinear expectation
G-expectation
60H10
60H30
G-normal distribution
G-Brownian motion
G-heat equation
Sublinear expectation
60H05
60E07
49L25
35K55
60E05
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Summary:We obtain the viscosity solution of the G-heat equation with the initial condition ϕ(x)=xn for each integer n≥1 using the method of G-Brownian motion.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2012.08.002