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Set-indexed processes with independent increments

Author

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  • Balan, R. M.

Abstract

Set-indexed process with independent increments are described by 'convolution systems'; the construction of such a process is given using Kolmogorov's extension theorem. When we specialize to the case of Lévy processes, we obtain a double characterization in terms of their characteristic functions and in terms of their generators.

Suggested Citation

  • Balan, R. M., 2002. "Set-indexed processes with independent increments," Statistics & Probability Letters, Elsevier, vol. 59(4), pages 415-424, October.
    • Handle: RePEc:eee:stapro:v:59:y:2002:i:4:p:415-424
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    References listed on IDEAS

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    1. Adler, R. J. & Monrad, D. & Scissors, R. H. & Wilson, R., 1983. "Representations, decompositions and sample function continuity of random fields with independent increments," Stochastic Processes and their Applications, Elsevier, vol. 15(1), pages 3-30, June.
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    Cited by:

    1. Herbin, Erick & Merzbach, Ely, 2013. "The set-indexed Lévy process: Stationarity, Markov and sample paths properties," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1638-1670.

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