Open Access
Issue
ESAIM: PS
Volume 30, 2026
Page(s) 49 - 76
DOI https://doi.org/10.1051/ps/2025017
Published online 11 February 2026
  1. J.O. Ramsay and B.W. Silverman, Functional Data Analysis. Springer (2005). [Google Scholar]
  2. R.G. Ghanem and P.D. Spanos, Stochastic Finite Elements: A Spectral Approach. Courier Corporation (2003). [Google Scholar]
  3. J. Dauxois, A. Pousse and Y. Romain, Asymptotic theory for the principal component analysis of a vector random function: some applications to statistical inference. J. Multivariate Anal. 12 (1982) 136–154. [Google Scholar]
  4. T. Hsing and R.L. Eubank, Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators, vol. 997. Wiley Online Library (2015). [Google Scholar]
  5. M. Loeve, Probability theory, Vol. II. Graduate Texts Math. 46 (1978) 0–387. [Google Scholar]
  6. J.R. Red-Horse and R.G. Ghanem, Elements of a function analytic approach to probability. Int. J. Numer. Methods Eng. 80 (2009) 689–716. [Google Scholar]
  7. O. Kallenberg, Random Measures, Theory and Applications. Springer (2017). [Google Scholar]
  8. P. Morando, Mesures aléatoires. Semin. Probab. Strasbourg 3 (1969) 190–229. [Google Scholar]
  9. M. Rao, Random and Vector Measures. World Scientific Publishing (2012). [Google Scholar]
  10. M. Thornett, A class of second-order stationary random measures. Stoch. Processes Appl. 8 (1979) 323–334. [Google Scholar]
  11. I. Borisov and A.A. Bystrov, Constructing a stochastic integral of a nonrandom function without orthogonality of the noise. Theory Probab. Appl. 50 (2006) 53–74. [Google Scholar]
  12. I. Kruk, F. Russo, and C.A. Tudor. Wiener integrals, Malliavin calculus and covariance measure structure. J. Funct. Anal. 249 (2007) 92–142. [Google Scholar]
  13. R. Fortet, Vecteurs, fonctions et distributions aleatoires dans les espaces de Hilbert: Analyse harmonique & prevision. Hermes (1995). [Google Scholar]
  14. I.M. Gelfand and N.I. Vilenkin, Generalized functions, Vol. 4 of Applications of Harmonic Analysis. Academic Press, New York (1964). [Google Scholar]
  15. K. Ito, Stationary random distributions. Mem. Coll. Sci. Univ. Kyoto Ser. A: Math. 28 (1954) 209–223. [Google Scholar]
  16. R. Meidan, Reproducing-kernel Hilbert spaces of distributions and generalized stochastic processes. SIAM J. Math. Anal. 10 (1979) 62–70. [Google Scholar]
  17. R. Carrizo Vergara, Generalized stochastic processes: linear relations to White Noise and orthogonal representations. Commun. Math. Statist. (2025) https://doi.org/10.1007/s40304-025-00461-6 [Google Scholar]
  18. X. Bay and J.-C. Croix, Karhunen-Loeve decomposition of Gaussian measures on Banach spaces. Probab. Math. Statist. 39 (2019) 279–297. [Google Scholar]
  19. B.S. Rajput, On Gaussian measures in certain locally convex spaces. J. Multivariate Anal. 2 (1972) 282–306. [Google Scholar]
  20. G. Peccati and J.-R. Pycke, Decompositions of stochastic processes based on irreducible group representations. Theory Probab. Appl. 54 (2010) 217–245. [Google Scholar]
  21. W.F. Donoghue, Distributions and Fourier Transform. Academic Press (1969). [Google Scholar]
  22. L. Schwartz, Theorie des Distributions. Hermann, Paris (1966). [Google Scholar]
  23. N. Bourbaki, Integration. Hermann (1965). [Google Scholar]
  24. M. Reed and B. Simon, Methods of Modern Mathematical Analysis: Functional Analysis. Academic Press, Singapore (1980). [Google Scholar]
  25. T. Soong, Random Differential Equations in Science and Engineering. Academic Press (1973). [Google Scholar]
  26. C. Brislawn, Traceable integral kernels on countably generated measure spaces. Pac. J. Math. 150 (1991) 229–240. [Google Scholar]
  27. J. Kupka, The Caratheodory extension theorem for vector valued measures. Proc. Am. Math. Soc. 72 (1978) 57–61. [Google Scholar]
  28. W. Rudin, Real and complex Analysis, 3rd edn. McGraw-Hill Book Company (1987). [Google Scholar]
  29. G.B. Folland, Real Analysis: Modern Techniques and their applications, Vol. 40. John Wiley & Sons (1999). [Google Scholar]
  30. N. Dunford and J.T. Schwartz, Linear Operators. Part I: General Theory, vol. 7. Interscience Publishers, New York (1958). [Google Scholar]
  31. R. Carrizo Vergara. Development of geostatistical models using stochastic partial differential equations. PhD thesis, MINES ParisTech, PSL Research University (2018). [Google Scholar]
  32. G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions. Cambridge University Press (2014). [Google Scholar]
  33. M. Veraar, The stochastic Fubini theorem revisited. Stochastics 84 (2012) 543–551. [Google Scholar]
  34. A.M. Yaglom, Correlation Theory of Stationary and Related Random Functions I: Basic Results. Springer-Verlag, New York (1987). [Google Scholar]
  35. F. Collet, F. Leisen and S. Thorbjørnsen, Completely random measures and Levy bases in free probability. Electron. J. Probab. 26 (2021) 1–41. [CrossRef] [MathSciNet] [Google Scholar]
  36. J. Kingman, Completely random measures. Pac. J. Math. 21 (1967) 59–78. [Google Scholar]
  37. R. Passeggeri, On the extension and kernels of signed bimeasures and their role in stochastic integration. arXiv preprint arXiv:2009.10657v2 (2025). [Google Scholar]
  38. S. Ken-Iti, Levy Processes and Infinitely Divisible Distributions, Vol. 68. Cambridge University Press (1999). [Google Scholar]
  39. D. Hackmann, Karhunen-Loeve expansions of Levy processes. Commun. Statist. Theory Methods 47 (2018) 5675–5687. [Google Scholar]
  40. J. Horowitz, Gaussian random measures. Stoch. Processes Appl. 22 (1986) 129–133. [Google Scholar]
  41. B. Øksendal, Stochastic Differential Equations: An Introduction with Applications, 5th edn. Springer-Verlag (2003). [Google Scholar]
  42. D.J. Daley and D. Vere-Jones, An Introduction to the Theory of Point Processes, vol. I of Elementary Theory and Methods. Springer Science & Business Media (2006). [Google Scholar]
  43. B.S. Rajput and J. Rosinski, Spectral representations of infinitely divisible processes. Probab. Theory Related Fields 82 (1989) 451–487. [Google Scholar]
  44. D.R. Cox, Some statistical methods connected with series of events. J. Roy. Statist. Soc. Ser. B (Methodological) 17 (1955) 129–157. [Google Scholar]
  45. J. Møller, A.R. Syversveen and R.P. Waagepetersen, Log-Gaussian Cox processes. Scand. J. Statist. 25 (1998) 451–482. [Google Scholar]
  46. V. Anh, J. Angulo and M. Ruiz-Medina, Possible long-range dependence in fractional random fields. J. Statist. Planning Inference 80 (1999) 95–110. [Google Scholar]
  47. R. Gay and C. Heyde, On a class of random field models which allows long range dependence. Biometrika 77 (1990) 401–403. [Google Scholar]
  48. M. Zahle, Integration with respect to fractal functions and stochastic calculus. I. Probab. Theory Related Fields 111 (1998) 333–374. [Google Scholar]
  49. D. Williams, Probability with Martingales. Cambridge University Press (1990). [Google Scholar]
  50. O. Sauri and A.E.D. Veraart, Nonparametric estimation of trawl processes: Theory and Applications. arXiv preprint arXiv:2209.05894v2 (2024). [Google Scholar]
  51. A.E. Veraart, Modeling, simulation and inference for multivariate time series of counts using trawl processes. J. Multivariate Anal. 169 (2019) 110–129. [Google Scholar]
  52. J. Diestel and B. Faires, On vector measures. Trans. Am. Math. Soc. 198 (1974) 253–271. [Google Scholar]
  53. J.L. Doob, Stochastic Processes, vol. 7. Wiley New York (1953). [Google Scholar]

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