Abstract
In this note we prove a diffusion approximation result for an elliptic SPDE with and additive white noise. The proof is based on the continuity property of the map that sends the solution of the linear problem into the general solution. We also get a large deviation result as a direct corollary of the continuity property.
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References
P. Billingsley: Convergence of probability measures. New York. Wiley and Sons, 1979.
R. Buckdahn and E. Pardoux: Monotonicity methods for white noise driven SPDEs. In: M. Pinski (ed.), Diffusion processes and related topics in Analysis, vol. I, pp. 219–233. Boston Basel Stuttgart. Birkhaüser 1990.
R. Carmona and J.P. Fouque: A diffusion approximation result for two parameter processes. Probab. Theory Rel. Fields 98, pp. 277–298, 1994.
J.D. Deuschel and D. Stroock: An introduction to the theory of large deviations. New York. Academic Press, 1988.
C. Donati-Martin: Quasi-linear elliptic stochastic partial differential equation. Markov property. Stochastics 41, pp. 219–240, 1992.
J. Gaiambos: Advanced probability theory. New York and Basel. Marcel Dekker, Inc. 1988.
D. Nualart and E. Pardoux: Second order stochastic differential equations with Dirichlet boundary conditions. Stochastics 39, pp. 1–24, 1991
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© 1996 Birkhäuser Boston
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Tindel, S. (1996). Diffusion approximation for elliptic stochastic differential equations. In: Körezlioğlu, H., Øksendal, B., Üstünel, A.S. (eds) Stochastic Analysis and Related Topics V. Progress in Probability, vol 38. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2450-1_13
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DOI: https://doi.org/10.1007/978-1-4612-2450-1_13
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-7541-1
Online ISBN: 978-1-4612-2450-1
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