Exit time and invariant measure asymptotics for small noise constrained diffusions |
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Authors: | Anup Biswas Amarjit Budhiraja |
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Institution: | a Centre for Applicable Mathematics, Tata Institute of Fundamental Research, Post Bag no 03, Chikkabommasandra, Bangalore-560065, Indiab Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, NC 27599, USA |
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Abstract: | Constrained diffusions, with diffusion matrix scaled by small ?>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 ?→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 ?2 these moments are shown to asymptotically coalesce at an exponential rate. |
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Keywords: | primary 60F10 60J60 60J25 secondary 93E15 90B15 |
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