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- W1971103980 abstract "This paper considers solutions of $0 = varepsilon sum_{i,j} {a_{i,j}^varepsilon } (x)u_{x_i x_j }^varepsilon + sum_i {b_i^varepsilon } (x)u_i^varepsilon $ in a bounded domain $Omega $ for which $sup _Omega | {u^varepsilon } |$ is bounded in $varepsilon > 0$. We assume that $a^varepsilon to a^0 $, $b^varepsilon to b^0 $ and that all solutions of the ODE $dot x = b^0 (x),x(0) in Omega $ converge to a single linearly asymptotically stable critical point in $Omega $ without leaving $Omega $. We give a proof, based on the standard probabilistic interpretation of $u^varepsilon $, of an exponential leveling property: $sup _{x,y in K} | {u^varepsilon (x) - u^varepsilon (y)} | leq e^{{ - delta }/{varepsilon }} $ for some $delta > 0$ which depends on the compact set $K subseteq Omega $." @default.
- W1971103980 created "2016-06-24" @default.
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- W1971103980 date "1982-07-01" @default.
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- W1971103980 title "Exponential Leveling for Stochastically Perturbed Dynamical Systems" @default.
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- W1971103980 doi "https://doi.org/10.1137/0513035" @default.
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