Linear transformations of Gaussian measures

Linear transformations of Gaussian measures
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Trans. Amer. Math. Soc. 122 (1966), 98-111

DOI: https://doi.org/10.1090/S0002-9947-1966-0199888-6

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References

C. Raymond Adams and James A. Clarkson, Properties of functions $f(x,y)$ of bounded variation, Trans. Amer. Math. Soc. 36 (1934), no. 4, 711–730. MR 1501762, DOI 10.1090/S0002-9947-1934-1501762-6

Continuity and Hölder’s conditions for sample functions of stationary Gaussian processes

R. H. Cameron and W. T. Martin, Transformations of Wiener integrals under a general class of linear transformations, Trans. Amer. Math. Soc. 58 (1945), 184–219. MR 13240, DOI 10.1090/S0002-9947-1945-0013240-1
J. A. Clarkson, On double Riemann-Stieltjes integrals, Bull. Amer. Math. Soc. 39 (1933), no. 12, 929–936. MR 1562763, DOI 10.1090/S0002-9904-1933-05771-3
J. L. Doob, Stochastic processes, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1953. MR 0058896
Charles Albert Fischer, Linear functionals of $N$-spreads, Ann. of Math. (2) 19 (1917), no. 1, 37–43. MR 1502511, DOI 10.2307/1967663
Michel Loève, Probability theory, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-New York-London, 1960. 2nd ed. MR 0123342

Linear integral equations

I. E. Segal, Distributions in Hilbert space and canonical systems of operators, Trans. Amer. Math. Soc. 88 (1958), 12–41. MR 102759, DOI 10.1090/S0002-9947-1958-0102759-X
Dale E. Varberg, On equivalence of Gaussian measures, Pacific J. Math. 11 (1961), 751–762. MR 126861
Dale E. Varberg, Gaussian measures and a theorem of T. S. Pitcher, Proc. Amer. Math. Soc. 13 (1962), 799–807. MR 142150, DOI 10.1090/S0002-9939-1962-0142150-X

Modern analysis

D. A. Woodward, A general class of linear transformations of Wiener integrals, Trans. Amer. Math. Soc. 100 (1961), 459–480. MR 131163, DOI 10.1090/S0002-9947-1961-0131163-3
William L. Root, Singular Gaussian measures in detection theory, Proc. Sympos. Time Series Analysis (Brown Univ., 1962) Wiley, New York, 1963, pp. 292–315. MR 0148126