Anni Toivola | Searcharxiv

arXiv2015

On fractional smoothness and $L_p$-approximation on the Gaussian space

We consider Gaussian Besov spaces obtained by real interpolation and Riemann-Liouville operators of fractional integration on the Gaussian space and relate the fractional smoothness of a functional to the regularity of its heat extension. The results are applied to study an approximation problem in $L_p$ for $2\le p<\infty$ for stochastic integrals with respect to the $d$-dimensional (geometric) Brownian motion.

math.PR↗

arXiv2010

Weak convergence of error processes in discretizations of stochastic integrals and Besov spaces

We consider weak convergence of the rescaled error processes arising from Riemann discretizations of certain stochastic integrals and relate the $L_p$-integrability of the weak limit to the fractional smoothness in the Malliavin sense of the stochastic integral.

math.PR↗