manuscripta mathematica

, Volume 45, Issue 2, pp 115–125 | Cite as

On weak convergence of stocastic processes with Lusin path spaces

  • Heinz Cremers
  • Dieter Kadelka


Under the assumption that a sequence of stochastic processes has paths in a Lusin function space we can prove the following. If convergence in the path space implies stochastic convergence, then tightness and convergence of the finite dimensional distributions of the stochastic processes are sufficient for weak convergence. The result in many cases implies a unification of the weak convergence proof. Demonstrably, such cases are C, D, Lipα, Lp and Δ, the space of distribution functions of finite measures.


Distribution Function Stochastic Process Function Space Number Theory Algebraic Geometry 
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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Heinz Cremers
    • 1
  • Dieter Kadelka
    • 1
  1. 1.Institut für Mathematische StatistikUniversität KarlsruheKarlsruheBRD

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