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For further reading on the martingale problem and differential equations a good source is
D.W. Stroock, S.R.S. Varadan, "Multidimensional Diffusion Processes" (Springer-Verlag, New York, 1979).
For Krylov's theorem consult
N.V. Krylov, "Controlled Diffusion Processes" (Springer-Verlag, New York, 1980).
N.V. Krylov, Sequences of convex functions and estimates of the maximum of the solution of a parabolic equation, Siberian Math J. 17(2) (1976); 226–236 (English translation).
For non-standard probability consult
H.J. Keisler, An infinitesimal approach to stochastic analysis, 1980 (yet to be published).
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© 1983 Springer-Verlag
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Kosciuk, S.A. (1983). Stochastic solutions to partial differential equations. In: Hurd, A.E. (eds) Nonstandard Analysis-Recent Developments. Lecture Notes in Mathematics, vol 983. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0065335
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DOI: https://doi.org/10.1007/BFb0065335
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