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Stochastic solutions to partial differential equations

Part of the Lecture Notes in Mathematics book series (LNM,volume 983)

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References

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).

    Google Scholar 

For Krylov's theorem consult

  • N.V. Krylov, "Controlled Diffusion Processes" (Springer-Verlag, New York, 1980).

    CrossRef  MATH  Google Scholar 

  • 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).

    CrossRef  MathSciNet  MATH  Google Scholar 

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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  • Print ISBN: 978-3-540-12279-1

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