Abstract
We will investigate the problem of characterizing the class of such orthonormal bases inL 2([0, 1]) with respect to which all quasi-martingales become integrable in the sense of noncausal integration. As an application of the results, we will show that the integral of noncausal type is a natural generalization of symmetric integrals.
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Ogawa, S. The stochastic integral of noncausal type as an extension of the symmetric integrals. Japan J. Appl. Math. 2, 229–240 (1985). https://doi.org/10.1007/BF03167046
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DOI: https://doi.org/10.1007/BF03167046