Commutation of variation and dual projection

Neal, David

doi:10.1090/S0002-9939-1995-1242100-0

Commutation of variation and dual projection
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by David Neal

Proc. Amer. Math. Soc. 123 (1995), 1591-1595

DOI: https://doi.org/10.1090/S0002-9939-1995-1242100-0

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Abstract:

For a raw process of integrable variation V, taking values in a Banach space E having the Radon-Nikodyn property, the variation of the predictable (optional) dual projection is the predictable (optional) dual projection of the variation. An analogous result holds for the associated stochastic measures. The result is applied to the stochastic integral of a real, optional process H with respect to V when V is adapted.

References

James K. Brooks and Nicolae Dinculeanu, Lebesgue-type spaces for vector integration, linear operators, weak completeness and weak compactness, J. Math. Anal. Appl. 54 (1976), no. 2, 348–389. MR 420266, DOI 10.1016/0022-247X(76)90207-9
Claude Dellacherie and Paul-André Meyer, Probabilities and potential, North-Holland Mathematics Studies, vol. 29, North-Holland Publishing Co., Amsterdam-New York, 1978. MR 521810
N. Dinculeanu, Vector measures, Hochschulbücher für Mathematik, Band 64, VEB Deutscher Verlag der Wissenschaften, Berlin, 1966. MR 0206189
Nicolae Dinculeanu, Vector-valued stochastic processes. I. Vector measures and vector-valued stochastic processes with finite variation, J. Theoret. Probab. 1 (1988), no. 2, 149–169. MR 938256, DOI 10.1007/BF01046932
Nicolae Dinculeanu, Vector-valued stochastic processes. I. Vector measures and vector-valued stochastic processes with finite variation, J. Theoret. Probab. 1 (1988), no. 2, 149–169. MR 938256, DOI 10.1007/BF01046932

Vector-valued stochastic processes

Projections and dual projections

Nicolae Dinculeanu, Vector-valued stochastic processes. V. Optional and predictable variation of stochastic measures and stochastic processes, Proc. Amer. Math. Soc. 104 (1988), no. 2, 625–631. MR 962839, DOI 10.1090/S0002-9939-1988-0962839-8
David Neal, Characterization of ${\scr O}$-summable processes, J. Theoret. Probab. 5 (1992), no. 3, 585–596. MR 1176440, DOI 10.1007/BF01060438