Exit time and invariant measure asymptotics for small noise constrained diffusions
AbstractConstrained diffusions, with diffusion matrix scaled by small ϵ>0, in a convex polyhedral cone G⊂Rk, are considered. Under suitable stability assumptions small noise asymptotic properties of invariant measures and exit times from domains are studied. Let B⊂G be a bounded domain. Under conditions, an “exponential leveling” property that says that, as ϵ→0, the moments of functionals of exit location from B, corresponding to distinct initial conditions, coalesce asymptotically at an exponential rate, is established. It is shown that, with appropriate conditions, difference of moments of a typical exit time functional with a sub-logarithmic growth, for distinct initial conditions in suitable compact subsets of B, is asymptotically bounded. Furthermore, as initial conditions approach 0 at a rate ϵ2 these moments are shown to asymptotically coalesce at an exponential rate.
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Bibliographic InfoArticle provided by Elsevier in its journal Stochastic Processes and their Applications.
Volume (Year): 121 (2011)
Issue (Month): 5 ()
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description
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- Borkar, V. S., 2003. "Dynamic programming for ergodic control with partial observations," Stochastic Processes and their Applications, Elsevier, vol. 103(2), pages 293-310, February.
- Dupuis, Paul & Ramanan, Kavita, 2002. "A time-reversed representation for the tail probabilities of stationary reflected Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 98(2), pages 253-287, April.
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