Functional and Banach Space Stochastic Calculi: Path-Dependent Kolmogorov Equations Associated with the Frame of a Brownian Motion

DOI10.1007/978-3-319-23425-0_2zbMath1338.60138OpenAlexW2224454562MaRDI QIDQ2801789

Francesco Russo, Andrea Cosso

Publication date: 22 April 2016

Published in: Stochastics of Environmental and Financial Economics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-23425-0_2

zbMATH Keywords

path-dependent Kolmogorov equationswindow Brownian motioncalculus via regularizationBanach space stochastic calculusfunctional Itō/path-dependent calculusstrong-viscosity solutions

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Brownian motion (60J65) Applications of stochastic analysis (to PDEs, etc.) (60H30) Stochastic integrals (60H05) Second-order parabolic equations (35K10) Viscosity solutions to PDEs (35D40) Strong solutions to PDEs (35D35)

Related Items (7)

A weak version of path-dependent functional Itô calculus ⋮ Functional Itô versus Banach space stochastic calculus and strict solutions of semilinear path-dependent equations ⋮ About classical solutions of the path-dependent heat equation ⋮ Weak differentiability of Wiener functionals and occupation times ⋮ Strong-viscosity solutions: classical and path-dependent PDEs ⋮ Calculus via regularizations in Banach spaces and Kolmogorov-type path-dependent equations ⋮ Crandall-Lions viscosity solutions for path-dependent PDEs: the case of heat equation

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