Recent interest in the reflected quasipotential comes from the queueing theory literature, specifically the analysis of so-called $$(b,A,D)$$ ( b , A , D ) reflected Brownian motion where it is the large deviation rate function for the stationary distribution. Our purpose here is to characterize the reflected quasipotential in terms of a first-order Hamilton–Jacobi equation. Using conventional dynamic programming ideas, along with a complementarity problem formulation of the effect of the Skorokhod map on absolutely continuous paths, we will derive necessary conditions in the form of viscosity-sense boundary conditions. It turns out that even with these boundary conditions solutions are not unique. Thus a unique characterization needs to refer to some additional property of $$V(\cdot )$$ V ( · ) . We establish such a characterization in two dimensions.
Applied Mathematics and Optimization – Springer Journals
Published: Dec 1, 2015
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera