Summary
This paper concerns asymptotic properties of the stationary density associated with small-noise diffusion processes, such as considered in the well-known work of Ventcel and Freidlin [12]. We assume that the origin is a globally attracting asymptotically stable equilibrium point of the underlying deterministic flow. For a bounded domain D, containing the origin, we derive estimates which establish the asymptotic independence, as the size of the noise vanishes, of the equilibrium density in D from the coefficients of the process outside D. These results are applied to generalize a result of Sheu [10] on an asymptotic representation of the equilibrium density.
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Day, M.V. Localization results for densities associated with stable small-noise diffusions. Probab. Th. Rel. Fields 77, 457–470 (1988). https://doi.org/10.1007/BF00319299
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DOI: https://doi.org/10.1007/BF00319299
Keywords
- Stochastic Process
- Probability Theory
- Diffusion Process
- Equilibrium Point
- Statistical Theory