4,172 research outputs found
Second-Order Elliptic Integro-Differential Equations: Viscosity Solutions' Theory Revisited
The aim of this work is to revisit viscosity solutions' theory for
second-order elliptic integro-differential equations and to provide a general
framework which takes into account solutions with arbitrary growth at infinity.
Our main contribution is a new Jensen-Ishii's Lemma for integro-differential
equations, which is stated for solutions with no restriction on their growth at
infinity. The proof of this result, which is of course a key ingredient to
prove comparison principles, relies on a new definition of viscosity solution
for integro-differential equation (equivalent to the two classical ones) which
combines the approach with test-functions and sub-superjets
Small Noise Asymptotics for Invariant Densities for a Class of Diffusions: A Control Theoretic View (with Erratum)
The uniqueness argument in the proof of Theorem 5, p. 483, of "Small noise
asymptotics for invariant densities for a class of diffusions: a control
theoretic view, J. Math. Anal. and Appl. (2009) " is flawed. We give here a
corrected proof.Comment: 23 pages; Journal of Mathematical Analysis and Applications, 200
- …