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Sobolev spaces Hγ(M), γ ∈ R, M ⊂ Rd
M-bounded
Def If n ∈ N, then Hn - all generalized functions with derivatives up to
n-th order belong to L2(M); kuk 2Hn = P |α | ≤n R
M
|Dαu| 2dx
The use of systems of stochastic PDEs as priors for multivariate models with discrete structures
Gaussian distribution multivariate stochastic PDEs discrete structures
2012/9/17
A challenge in multivariate problems with discrete structures is the inclusion of prior information that may di er in each separate structure. A particular example of this is seismic amplitude versus ...
An Exact Connection between two Solvable SDEs and a Non Linear Utility Stochastic PDEs
forward utility performance criteria horizon-unbiased utility
2010/10/20
The paper proposes a new approach to consistent stochastic utilities, also called forward dynamic utility, recently introduced by M. Musiela and T. Zariphopoulou. These utilities satisfy a property of...
Backward Stochastic PDEs related to the utility maximization problem
Backward Stochastic PDEs utility maximization problem
2010/12/20
We study utility maximization problem for general utility functions using dynamic programming approach. We consider an incomplete financial market model, where the dynamics of asset prices are descri...