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A probabilistic approach to one class of nonlinear differential equations
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  • Published: March 1991

A probabilistic approach to one class of nonlinear differential equations

  • E. B. Dynkin1 

Probability Theory and Related Fields volume 89, pages 89–115 (1991)Cite this article

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Summary

We establish connections between positive solutions of one class of nonlinear partial differential equations and hitting probabilities and additive functionals of superdiffusion processes. As an application, we improve results on superprocesses by using the recent progress in the theory of removable singularities for differential equations.

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Authors and Affiliations

  1. Department of Mathematics, Cornell University, White Hall, 14853, Ithaca, NY, USA

    E. B. Dynkin

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  1. E. B. Dynkin
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Additional information

Partially supported by National Science Foundation Grant DMS-8802667

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Cite this article

Dynkin, E.B. A probabilistic approach to one class of nonlinear differential equations. Probab. Th. Rel. Fields 89, 89–115 (1991). https://doi.org/10.1007/BF01225827

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  • Received: 06 June 1990

  • Revised: 22 February 1991

  • Issue Date: March 1991

  • DOI: https://doi.org/10.1007/BF01225827

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
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