Quasi-sure convergence theorem in $p$-variation distance for stochastic differential equations

H. Boedihardjo; Z. Qian

Quasi-sure convergence theorem in $p$-variation distance for stochastic differential equations

Probability 2012-04-26 v1

Authors: H. Boedihardjo , Z. Qian

Abstract

In this paper by calculating carefully the capacities (defined by high order Sobolev norms on the Wiener space) for some functions of Brownian motion, we show that the dyadic approximations of the sample paths of the Brownian motion converge in the $p$ -variation distance to the Brownian motion except for a slim set (i.e. except for a zero subset with respect to the capacity on the Wiener space of any order). This presents a way for studying quasi-sure properties of Wiener functionals by means of the rough path analysis.

Keywords

stochastic differential equations brownian motion p-variation distance quasi-sure convergence capacity sobolev norms wiener space rough path analysis

Cite

@article{arxiv.1204.5673,
  title  = {Quasi-sure convergence theorem in $p$-variation distance for stochastic differential equations},
  author = {H. Boedihardjo and Z. Qian},
  journal= {arXiv preprint arXiv:1204.5673},
  year   = {2012}
}

Quasi-sure convergence theorem in $p$-variation distance for stochastic differential equations

Abstract

Keywords

Cite

Related papers