Itô's calculus under sublinear expectations via regularity of PDEs and rough paths

DOI10.1016/j.spa.2017.08.008zbMath1390.60160OpenAlexW2752561900MaRDI QIDQ1747795

Xin Guo, Chen Pan

Publication date: 27 April 2018

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spa.2017.08.008

zbMATH Keywords

martingale problemstochastic integralItô's formulafully nonlinear PDEsrough path theorynonlinear expectation

Mathematics Subject Classification ID

Optimal stochastic control (93E20) Martingales with continuous parameter (60G44) Stochastic integrals (60H05) Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations (35K61)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quasi-sure stochastic analysis through aggregation
• Pathwise construction of stochastic integrals
• Wellposedness of second order backward SDEs
• Martingale representation theorem for the \(G\)-expectation
• Curvilinear integrals along enriched paths
• Stochastic integration and \(L^ p-\)theory of semimartingales
• Differential equations driven by rough signals
• Controlling rough paths
• Nonlinear expectations and nonlinear Markov chains
• Second-order backward stochastic differential equations and fully nonlinear parabolic PDEs
• Stochastic Differential Games and Viscosity Solutions of Hamilton–Jacobi–Bellman–Isaacs Equations
• Classical solutions of fully nonlinear, convex, second-order elliptic equations
• User’s guide to viscosity solutions of second order partial differential equations
• G-Brownian Motion as Rough Paths and Differential Equations Driven by G-Brownian Motion
• Diffusion processes with continuous coefficients, I
• A course on rough paths. With an introduction to regularity structures