Bernoulli

  • Bernoulli
  • Volume 6, Number 4 (2000), 653-665.

Weak approximation of the Brownian sheet from a Poisson process in the plane

Xavier Bardina and Maria Jolis

Full-text: Open access

Abstract

We show an approximation in law of the Brownian sheet by processes constructed from the Poisson process in the plane. This result was inspired by a similar result of Stroock in the one-parameter case.

Article information

Source
Bernoulli, Volume 6, Number 4 (2000), 653-665.

Dates
First available in Project Euclid: 8 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1081449599

Mathematical Reviews number (MathSciNet)
MR2001j:60098

Zentralblatt MATH identifier
0965.60064

Keywords
two-parameter Poisson process two-parameter Wiener process weak convergence

Citation

Bardina, Xavier; Jolis, Maria. Weak approximation of the Brownian sheet from a Poisson process in the plane. Bernoulli 6 (2000), no. 4, 653--665. https://projecteuclid.org/euclid.bj/1081449599


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References

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  • [2] Cairoli, R. and Walsh, J.B. (1975) Stochastic integrals in the plane. Acta Math., 134, 111-183.
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  • [4] Stroock, D. (1982) Lectures on Topics in Stochastic Differential Equations. Berlin: Springer-Verlag.
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