A Wiener Chaos Approach to Hyperbolic SPDEs

作者：Kalpinelli E A; Frangos N E^*; Yannacopoulos A N

来源：Stochastic Analysis and Applications, 2011, 29(2): 237-258.

DOI：10.1080/07362994.2011.532023

• Generalized random elements
• Interest rate modelling
• Malliavin calculus
• Stochastic hyperbolic PDEs
• Weiner Chaos
• Weighted spaces

We construct generalized weighted Wiener chaos solutions for hyperbolic linear SPDEs driven by a cylindrical Brownian motion. Explicit conditions for the existence, uniqueness, and regularity of generalized (Wiener Chaos) solutions are established in Sobolev spaces. An equivalence relation between the Wiener Chaos solution and the traditional one is established. The Heath-Jarrow-Morton (HJM) forward rate model is used as an example to illustrate the general construction.

• 出版日期2011