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摘要
We estimate the variance of the value function for a random optimal control problem. The value function is the solution w (I mu) of a Hamilton-Jacobi equation with random Hamiltonian H(p,x,omega)=K(p)-V(x/I mu,omega) in dimension da parts per thousand yen2. It is known that homogenization occurs as I mu -> 0, but little is known about the statistical fluctuations of w (I mu) . Our main result shows that the variance of the solution w (I mu) is bounded by O(I mu/|logI mu|). The proof relies on a modified Poincar, inequality of Talagrand.
- 出版日期2012-10
