Khrennikov, A. Yu.; Kozyrev, S. V. Ultrametric random field. (English) Zbl 1154.60323 Infin. Dimens. Anal. Quantum Probab. Relat. Top. 9, No. 2, 199-213 (2006). Summary: Gaussian random field on general ultrametric space is introduced as a solution of pseudodifferential stochastic equation. Covariation of the introduced random field is computed with the help of wavelet analysis on ultrametric spaces. Notion of ultrametric Markovianity, which describes independence of contributions to random field from different ultrametric balls is introduced. We show that the random field under investigation satisfies this property. Cited in 19 Documents MSC: 60G15 Gaussian processes 60G60 Random fields 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 60H40 White noise theory 60J99 Markov processes Keywords:ultrametric analysis; random fields; pseudodifferential operators PDFBibTeX XMLCite \textit{A. Yu. Khrennikov} and \textit{S. V. Kozyrev}, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 9, No. 2, 199--213 (2006; Zbl 1154.60323) Full Text: DOI arXiv References: [1] DOI: 10.1070/IM1997v061n03ABEH000126 · Zbl 0896.60044 [2] DOI: 10.1142/1581 [3] Smolyanov O. G., Usp. Math. 31 pp 3– [4] DOI: 10.1016/j.acha.2005.02.001 · Zbl 1079.42028 [5] Yu. Khrennikov A., Russ. Math. Izv. 69 [6] DOI: 10.1070/IM2002v066n02ABEH000381 · Zbl 1016.42025 [7] DOI: 10.1007/BF02922099 · Zbl 1114.42015 [8] DOI: 10.1023/B:TAMP.0000018449.72502.6f · Zbl 1178.42039 [9] Kozyrev S. V., Proc. of the Stek. Math. Inst. 245 pp 154– [10] Kozyrev S. V., J. Math. Phys. 46 pp P.063302– [11] DOI: 10.1088/0264-9381/4/4/003 [12] DOI: 10.1016/0550-3213(88)90207-6 [13] DOI: 10.1088/0305-4470/32/50/301 · Zbl 0957.82034 [14] DOI: 10.1007/s100510051063 [15] DOI: 10.1142/S0217751X91002094 · Zbl 0733.53039 [16] DOI: 10.1007/978-94-015-8356-5 [17] DOI: 10.1007/978-94-009-1483-4 [18] DOI: 10.1201/9780203908167 [19] Khrennikov A., Russ. J. Math. Phys. 11 pp 45– [20] DOI: 10.1007/s00012-003-1806-4 · Zbl 1094.54004 [21] Khrennikov A., Classical and Quantum Mental Models and Freud’s Theory of Unconcious Mind (2002) [22] DOI: 10.1007/978-3-642-61856-7 [23] DOI: 10.1007/978-1-4612-1468-7 [24] DOI: 10.1007/978-94-011-2600-7 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.