| 概要 |
We present a stochastic approach to the single and double obstacle problems for the p-Laplacian operator. The stochastic processes from which we construct a sequence of approximations to the solution is of the kind tug-of-war with added noise. Solutions are uniform limits of solutions to discrete min-max problems that can be interpreted as the dynamic programming principle for appropriate tug-of-war games with noise. In these games, both players in addition to choosing their strategies, are also allowed to choose stopping times. The solutions to the double-obstacle problems are limits of values of these games, when the step-size controlling the single shift in the token's position, converges to 0.
This is joint work with Marta Lewicka and Luca Codenotti (Pittsburgh).
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