Albeverio, Sergio; Wu, Jianglun Euclidean random fields obtained by convolution from generalized white noise. (English) Zbl 0841.60091 J. Math. Phys. 36, No. 10, 5217-5245 (1995). Summary: We study Euclidean random fields \(X\) over \(\mathbb{R}^d\) of the form \(X = G * F\), where \(F\) is a generalized white noise over \(\mathbb{R}^d\) and \(G\) is an integral kernel. We give conditions for the existence of the characteristic functional and moment functions and we construct a convergent lattice approximation of \(X\). Finally, we perform the analytic continuation of the moment functions and the characteristic functional of \(X\), obtaining the corresponding relativistic functions on Minkowski space. Cited in 1 ReviewCited in 12 Documents MSC: 60K40 Other physical applications of random processes 83C99 General relativity Keywords:Euclidean random fields; characteristic functional; analytic continuation of the moment functions PDFBibTeX XMLCite \textit{S. Albeverio} and \textit{J. Wu}, J. Math. Phys. 36, No. 10, 5217--5245 (1995; Zbl 0841.60091) Full Text: DOI References: [1] DOI: 10.1016/0022-1236(73)90091-8 · Zbl 0252.60053 · doi:10.1016/0022-1236(73)90091-8 [2] DOI: 10.1016/0022-1236(73)90025-6 · Zbl 0273.60079 · doi:10.1016/0022-1236(73)90025-6 [3] DOI: 10.1007/BF01645738 · Zbl 0274.46047 · doi:10.1007/BF01645738 [4] DOI: 10.1007/BF01645738 · Zbl 0274.46047 · doi:10.1007/BF01645738 [5] DOI: 10.1007/BF01646614 · Zbl 0275.60120 · doi:10.1007/BF01646614 [6] DOI: 10.1007/BF01645941 · Zbl 0295.46064 · doi:10.1007/BF01645941 [7] DOI: 10.2307/1970988 · doi:10.2307/1970988 [8] DOI: 10.1007/BF01418123 · Zbl 0443.60099 · doi:10.1007/BF01418123 [9] DOI: 10.1063/1.525686 · doi:10.1063/1.525686 [10] DOI: 10.1007/BF01240220 · Zbl 0576.60097 · doi:10.1007/BF01240220 [11] DOI: 10.1007/BF01238808 · Zbl 0668.60093 · doi:10.1007/BF01238808 [12] DOI: 10.1016/0370-2693(86)91050-6 · doi:10.1016/0370-2693(86)91050-6 [13] DOI: 10.1016/0370-2693(87)91442-0 · doi:10.1016/0370-2693(87)91442-0 [14] DOI: 10.1016/0370-2693(88)91119-7 · doi:10.1016/0370-2693(88)91119-7 [15] DOI: 10.1016/0370-2693(88)91119-7 · doi:10.1016/0370-2693(88)91119-7 [16] DOI: 10.1063/1.530079 · Zbl 0780.60105 · doi:10.1063/1.530079 [17] DOI: 10.1007/BF02156537 · Zbl 0711.60058 · doi:10.1007/BF02156537 [18] DOI: 10.1016/0370-2693(89)91263-X · doi:10.1016/0370-2693(89)91263-X [19] DOI: 10.1016/0022-1236(89)90010-4 · Zbl 0696.60012 · doi:10.1016/0022-1236(89)90010-4 [20] DOI: 10.1016/0393-0440(93)90076-Q · Zbl 0780.60040 · doi:10.1016/0393-0440(93)90076-Q [21] DOI: 10.1016/0003-4916(89)90032-8 · Zbl 0698.60047 · doi:10.1016/0003-4916(89)90032-8 [22] DOI: 10.1016/0022-1236(92)90025-E · Zbl 0769.60009 · doi:10.1016/0022-1236(92)90025-E [23] Albeverio S., Acta Phys. Austr. Suppl. 26 pp 211– (1984) [24] DOI: 10.1007/BF01257412 · Zbl 0704.58059 · doi:10.1007/BF01257412 [25] DOI: 10.1007/BF01206886 · Zbl 0538.46053 · doi:10.1007/BF01206886 [26] DOI: 10.1007/BF01212281 · doi:10.1007/BF01212281 [27] DOI: 10.1090/S0002-9947-1965-0182061-4 · doi:10.1090/S0002-9947-1965-0182061-4 [28] DOI: 10.4153/CJM-1956-011-7 · Zbl 0070.13703 · doi:10.4153/CJM-1956-011-7 [29] DOI: 10.1016/0022-1236(88)90137-1 · Zbl 0639.60010 · doi:10.1016/0022-1236(88)90137-1 [30] DOI: 10.1007/BF01609839 · Zbl 0319.46060 · doi:10.1007/BF01609839 [31] DOI: 10.1007/BF01609839 · Zbl 0319.46060 · doi:10.1007/BF01609839 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.