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## Publications [#211578] of Ivan Matic

Papers Published

1. Ivan Matic, James Nolen, A sublinear variance bound for solutions of a random Hamilton-Jacobi equation, J Stat Phys, vol. 149 no. 2 (September, 2012), pp. 342-361, Springer, ISSN 149:342-361 [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 Hamilton-Jacobi 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 Hamilton-Jacobi equation, sublinear variance

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