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A criterion for right continuity of filtrations generated by group-valued additive processes

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  • Zapala, August M.

Abstract

Let X={X(t),t[set membership, variant]T} be a stochastic process with independent increments indexed by the multidimensional set of parameters T=(R+)q, q[greater-or-equal, slanted]1, taking values in a T0 topological Abelian group G. In this note, we give conditions under which the filtration , t[set membership, variant]T, generated by the process X is right continuous, i.e. for all t[set membership, variant]T.

Suggested Citation

  • Zapala, August M., 2003. "A criterion for right continuity of filtrations generated by group-valued additive processes," Statistics & Probability Letters, Elsevier, vol. 63(1), pages 79-87, May.
    • Handle: RePEc:eee:stapro:v:63:y:2003:i:1:p:79-87
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    References listed on IDEAS

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    1. Ossiander, Mina & Pyke, Ronald, 1985. "Lévy's Brownian motion as a set-indexed process and a related central limit theorem," Stochastic Processes and their Applications, Elsevier, vol. 21(1), pages 133-145, December.
    2. 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.
    3. Zapala, August M., 1991. "Regularization of trajectories for multiparameter additive processes in groups," Journal of Multivariate Analysis, Elsevier, vol. 36(2), pages 222-242, February.
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