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Stability of a class of transformations of distribution-valued processes and stochastic evolution equations

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Abstract

Stability of a class of linear transformations of distribution-valued stochastic processes is studied. Two types of applications to convergence of solutions of stochastic evolution equations are given. One of them, for the case of continuous limits, simplifies the tightness problem considerably due to a recent result of Aldous.

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Fernández, B., Gorostiza, L.G. Stability of a class of transformations of distribution-valued processes and stochastic evolution equations. J Theor Probab 5, 661–678 (1992). https://doi.org/10.1007/BF01058724

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Key Words

  • Distribution-valued process
  • stochastic evolution equation
  • semimartingale
  • convergence in distribution
  • nuclear space