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

DOI10.1016/j.na.2012.08.002zbMath1272.60034arXiv0907.2748OpenAlexW2083759962MaRDI QIDQ714486

Ming Shang Hu

Publication date: 11 October 2012

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0907.2748

zbMATH Keywords

\(G\)-Brownian motion\(G\)-heat equation

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Probability distributions: general theory (60E05) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Nonlinear parabolic equations (35K55) Applications of stochastic analysis (to PDEs, etc.) (60H30) Stochastic integrals (60H05) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25)

Related Items (6)

Uncertainty orders on the sublinear expectation space ⋮ Robust mean-variance hedging via \(G\)-expectation ⋮ G-Gaussian processes under sublinear expectations and \(q \)-Brownian motion in quantum mechanics ⋮ A worst-case risk measure by G-VaR ⋮ An efficient numerical method for forward-backward stochastic differential equations driven by \(G\)-Brownian motion ⋮ Explicit positive solutions to \(G\)-heat equations and the application to \(G\)-capacities

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Function spaces and capacity related to a sublinear expectation: application to \(G\)-Brownian motion paths
• Filtration consistent nonlinear expectations and evaluations of contingent claims
• Multi-dimensional \(G\)-Brownian motion and related stochastic calculus under \(G\)-expectation
• On the regularity theory of fully nonlinear parabolic equations: II
• User’s guide to viscosity solutions of second order partial differential equations
• Self-similar solutions of the second kind in nonlinear filtration

This page was built for publication: Explicit solutions of the \(G\)-heat equation for a class of initial conditions