A. Danelia, B. Dochviri, M. Shashiashvili
abstract:
Using the methods of stochastic analysis, new type energy estimates are obtained
in the theory of variational inequalities, in particular, for obstacle problems.
The derivation of these estimates is essentially based on our previously
obtained stochastic a priori estimates for Snell envelopes and on the connection
between the optimal stopping problem and a variational inequality. Using these
results, energy estimates are obtained for the solution of an obstacle problem
when only the continuity is required of the obstacle function $g=g(x)$.
Mathematics Subject Classification: 60G40, 35J85.
Key words and phrases: Variational inequality, Snell envelope, semimartingale, multidimensional diffusion process, optimal stopping problem.