Abstract
The optimal cost function associated to a stopping time problem for a dynamical system perturbed by an additive noise term with small positive coefficient ɛ satisfies a singularly perturbed variational inequality with an obstacle. Characteristic for this type of variational inequalities is the occurrence of a free boundary. Here we shall study the behaviour as ɛ → 0 of the solution and the free boundary of the variational inequality induced by a one-dimensional randomly perturbed differential equation. Our results are derived by standard techniques in the theory of asymptotic expansions and the maximum principle.
Keywords
- Variational Inequality
- Maximum Principle
- Free Boundary
- Singular Perturbation
- Differential Inequality
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Moet, H.J.K. (1979). Singular perturbation methods in a one-dimensional free boundary problem. In: Verhulst, F. (eds) Asymptotic Analysis. Lecture Notes in Mathematics, vol 711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062947
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DOI: https://doi.org/10.1007/BFb0062947
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