Explicit solutions of G-heat equation with a class of initial conditions by G-Brownian motion

Abstract

We obtain the viscosity solution of G-heat equation with the initial condition $\varphi (x)=x^n$ for each integer $n\ge 1$ using the method of G-Brownian motion.

12 pages

References in corpus (3)

• A New Central Limit Theorem under Sublinear Expectations
• G-Brownian Motion and Dynamic Risk Measure under Volatility Uncertainty
• Law of Large Numbers and Central Limit Theorem under Nonlinear Expectations

Cited by in corpus (4)

• G-Gaussian Processes under Sublinear Expectations and q-Brownian Motion in Quantum Mechanics
• Backward stochastic differential equations under super linear G-expectation and associated Hamilton-Jacobi-Bellman equations
• Semi-$G$-normal: a Hybrid between Normal and $G$-normal (Full Version)
• An Efficient Numerical Method for Forward-Backward Stochastic Differential Equations Driven by $G$-Brownian motion