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The local limit problem and Hölder-continuity
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  • Published: June 1989

The local limit problem and Hölder-continuity

  • Wolfgang Macht1 &
  • Werner Wolf1 

Probability Theory and Related Fields volume 82, pages 295–305 (1989)Cite this article

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  • 4 Citations

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Summary

The local limit problem is investigated for sequences (p n ) of probability densities with stable limit densitiesq α having characteristic exponent α∈(0, 2).

It is shown that certain continuity-properties (Hölder-continuity) are necessary and - under appropriate additional conditions-sufficient for\(\mathop {\sup }\limits_x |p_n (x) - q_\alpha (x)| \to 0\) asn→∞. In this sence the speed of convergence is also studied.

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Authors and Affiliations

  1. Sektion Mathematik, Technische Universität Dresden, Mommsenstr. 13, 8027, Dresden, German Democratic Republic

    Wolfgang Macht & Werner Wolf

Authors
  1. Wolfgang Macht
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  2. Werner Wolf
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Macht, W., Wolf, W. The local limit problem and Hölder-continuity. Probab. Th. Rel. Fields 82, 295–305 (1989). https://doi.org/10.1007/BF00354765

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  • Received: 21 June 1988

  • Issue Date: June 1989

  • DOI: https://doi.org/10.1007/BF00354765

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Keywords

  • Probability Density
  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Stable Limit
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