Worst case scenario analysis for elliptic problems with uncertainty

• Worst-case scenario analysis for elliptic PDE’s with uncertainty

Worst-case scenario analysis for elliptic PDE’s with uncertainty

• Worst-case scenario analysis for elliptic PDE’s with uncertainty

An adaptive algorithm for ordinary, stochastic and partial differential equations

• Adaptive methods,
• mesh refinement algorithm
• A posteriori error estimates
• Computational complexity

Adaptive Monte Carlo algorithms for stopped diffusion

• adaptive mesh refinement
• diffusion with boundary
• algorithm
• barrier option
• Monte Carlo method
• Weak approximation

Theory and methodology for estimation and control of errors due to modeling, approximation, and uncertainty

• Modeling error estimation
• Stochastic partial differential equations
• Adaptive modeling

Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation

• stochastic elliptic equation
• perturbation estimates
• Karhunen-Loeve expansion
• Finite elements
• Monte Carlo methods
• p × h-version
• k × h-version
• expected value
• error estimates
• Adaptive methods,
• error control

Convergence rates for adaptive weak approximation of stochastic differential equations

• Adaptive mesh refinement algorithm,
• Almost sure convergence
• Computational complexity
• Monte Carlo methods
• Stochastic differential equations