Functional quantization rate and mean regularity of processes with an application to Lévy processes

By Harald Luschgy, Gilles Pagès. 2006

54 citations recorded by the source corpus.

We investigate the connections between the mean pathwise regularity of stochastic processes and their L^r(P)-functional quantization rates as random variables taking values in some L^p([0,T],dt)-spaces (0 < p <= r). Our main tool is the Haar basis. We then emphasize that the derived functional quantization rate may be optimal (e.g., for Brownian motion or symmetric stable processes) so that the rate is optimal as a universal upper bound. As a first application, we establish the O((log N)^{-1/2}) upper bound for general Ito processes which include multidimensional diffusions. Then, we focus on the specific family of Levy processes for which we derive a general quantization rate based on the regular variation properties of its Levy measure at 0. The case of compound Poisson processes, which appear as degenerate in the former approach, is studied specifically: we observe some rates which are between the finite-dimensional and infinite-dimensional ``usual'' rates

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/931850ad22994e0cb47846833e5662700cb85443

Citations in the corpus

• MULTIFRACTIONAL STOCHASTIC VOLATILITY MODELS (2011, unknown): “However, since the regularity of mBm is known, one may use another, less precise, type of results: these yield an upper estimate on the rate of decay of the quantization error [53].”