• Corpus ID: 119645667

Weak error analysis via functional It\^o calculus

@article{Kovacs2016WeakEA,
  title={Weak error analysis via functional It\^o calculus},
  author={Mih'aly Kov'acs and Felix Lindner},
  journal={arXiv: Probability},
  year={2016}
}
We consider autonomous stochastic ordinary differential equations (SDEs) and weak approximations of their solutions for a general class of sufficiently smooth path-dependent functionals f. Based on tools from functional It\^o calculus, such as the functional It\^o formula and functional Kolmogorov equation, we derive a general representation formula for the weak error $E(f(X_T)-f(\tilde X_T))$, where $X_T$ and $\tilde X_T$ are the paths of the solution process and its approximation up to time T… 

References

SHOWING 1-10 OF 33 REFERENCES
Weak Error Estimates for Trajectories of SPDEs Under Spectral Galerkin Discretization
We consider stochastic semi-linear evolution equations which are driven by additive, spatially correlated, Wiener noise, and in particular consider problems of heat equation (analytic semigroup) and
Weak Convergence of Finite Element Approximations of Linear Stochastic Evolution Equations with Additive Lévy Noise
TLDR
An abstract framework to study weak convergence of numerical approximations of linear stochastic partial differential equations driven by additive L\'evy noise is presented and the weak rate of convergence is found to be twice the strong rate.
Weak Convergence Methods for Approximation of the Evaluation of Path-Dependent Functionals
TLDR
This work develops a numerical scheme so that an approximating sequence of path-dependent functionals $V^h$ converges to $V$, and denotes by $h$ the stepsize of the approximation sequence.
Weak Order for the Discretization of the Stochastic Heat Equation Driven by Impulsive Noise
AbstractWe study the approximation of the distribution of XT, where (Xt)t ∈ [0, T] is a Hilbert space valued stochastic process that solves a linear parabolic stochastic partial differential equation
Functional Ito calculus and stochastic integral representation of martingales
We develop a non-anticipative calculus for functionals of a continuous semimartingale, using an extension of the Ito formula to path-dependent functionals which possess certain directional
Weak convergence of finite element approximations of linear stochastic evolution equations with additive noise II. Fully discrete schemes
TLDR
An abstract framework for analyzing the weak error of fully discrete approximation schemes for linear evolution equations driven by additive Gaussian noise is presented and it is found that the rate of weak convergence is twice that of strong convergence.
Stochastic Integration by Parts and Functional Itô Calculus
This volume contains lecture notes from the courses given by Vlad Bally and Rama Cont at the Barcelona Summer School on Stochastic Analysis (July 2012). The notes of the course by Vlad Bally,
Weak approximation of martingale representations
...
...