White noise calculus and nonlinear filtering theory
Quite a while ago, \textit{A. V. Balakrishnan} stressed the inadequacies of modeling white noise with a Wiener process [see for example, Appl. Math. Optimization 1, 97-120 (1974; Zbl 0306.90056)] and suggested that white noise be represented by an additive only probability measure. His main concern was the problem of detecting signals. The present authors have been working for a while with the same additive model, but with an emphasis on the problem of filtering signals (see the bibliography of the paper being reviewed). They give here an overview of their work. To be brief, the conclusion is that, ''mutatis mutandis'', the same results can be obtained whether the noise is modeled as a Wiener process or as an additive only probability, but that, to reach that conclusion, much mathematics must be produced!
scientific article; zbMATH DE number 3936114