Publications [#287351] of James H. Nolen

Papers Published

1. Matic, I; Nolen, J, A Sublinear Variance Bound for Solutions of a Random Hamilton-Jacobi Equation, Journal of Statistical Physics, vol. 149 no. 2 (2012), pp. 342-361, Springer Nature, ISSN 0022-4715 [pdf], [doi]
   (last updated on 2024/04/22)

   Abstract:
   We estimate the variance of the value function for a random optimal control problem. The value function is the solution w ε of a Hamilton-Jacobi equation with random Hamiltonian H(p, x, ω)=K(p)-V(x/ε, ω) in dimension d ≥ 2. It is known that homogenization occurs as ε → 0, but little is known about the statistical fluctuations of w ε. Our main result shows that the variance of the solution w ε is bounded by O(ε/{pipe}log ε {pipe}). The proof relies on a modified Poincaré inequality of Talagrand. © 2012 Springer Science+Business Media, LLC.