English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The Heston stochastic volatility process, which is widely used as an assetprice model in mathematical finance, is a paradigm for a degenerate diffusionprocess where the degeneracy in the diffusion coefficient is proportional tothe square root of the distance to the boundary of the half-plane. Thegenerator of this process with killing, called the elliptic Heston operator, isa second-order, degenerate-elliptic partial differential operator whosecoefficients have linear growth in the spatial variables and where thedegeneracy in the operator symbol is proportional to the distance to theboundary of the half-plane. With the aid of weighted Sobolev spaces, we provesupremum bounds, a Harnack inequality, and H\"older continuity near theboundary for solutions to variational equations defined by the elliptic Hestonoperator, as well as H\"older continuity up to the boundary for solutions tovariational inequalities defined by the elliptic Heston operator. Inmathematical finance, solutions to obstacle problems for the elliptic Hestonoperator correspond to value functions for perpetual American-style options onthe underlying asset.

Boundary-degenerate elliptic operators and Holder continuity for solutions to variational equations and inequalities