Math @ Duke

Publications [#211578] of Ivan Matic
Papers Published
 Ivan Matic, James Nolen, A sublinear variance bound for solutions of a random HamiltonJacobi equation,
J Stat Phys, vol. 149 no. 2
(September, 2012),
pp. 342361, Springer, ISSN 149:342361 [2937]
(last updated on 2012/11/30)
Abstract: We estimate the variance of the value function for a random optimal control problem. The value function is the solution $w^\epsilon$ of a random HamiltonJacobi equation with random Hamiltonian $H(p,x,\omega) = K(p)  V(x/\epsilon,\omega)$ in dimension $d \geq 2$. It is known that homogenization occurs as $\epsilon \to 0$, but little is known about the statistical fluctuations of $w^\epsilon$. Our main result shows that the variance of the solution $w^\epsilon$ is bounded by $O(\epsilon/\log \epsilon)$. The proof relies on a modified Poincar\'e inequality of Talagrand.
Keywords: random HamiltonJacobi equation, sublinear variance


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