Abstract
In his talk [Dl] in the 1962 International Congress of Mathematicians, E.B. Dynkin noted that from being only a customer of analysis Markov processes became also a part of it supplying new results not proved by analytic methods beforehand. This especially became valid in problems connected with second-order elliptic and parabolic partial differential equations. The probabilistic intuition about the associated diffusion processes has since led to many results which were not known in partial differential equations and some of them have no proof based on PDE methods up to now.
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Kifer, Y. (1994). Harmonic Functions on Riemannian Manifolds: A Probabilistic Approach. In: Freidlin, M.I. (eds) The Dynkin Festschrift. Progress in Probability, vol 34. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0279-0_11
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DOI: https://doi.org/10.1007/978-1-4612-0279-0_11
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