Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Generalized stochastic integrals and equations


Author: Donald A. Dawson
Journal: Trans. Amer. Math. Soc. 147 (1970), 473-506
MSC: Primary 60.75
DOI: https://doi.org/10.1090/S0002-9947-1970-0261719-4
MathSciNet review: 0261719
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] J. L. Doob, Stochastic processes, Wiley, New York and Chapman & Hall, London, 1953. MR 15, 445. MR 0058896 (15:445b)
  • [2] R. M. Dudley, Sub-stationary processes, Pacific J. Math. 20 (1967), 207-215. MR 34 #8446. MR 0208637 (34:8446)
  • [3] X. Fernique, Processus linéaires, processus généralisés, Ann. Inst. Fourier (Grenoble) 17 (1967), no. 1, 1-92. MR 36 #4628. MR 0221576 (36:4628)
  • [4] A. Friedman, Generalized functions and partial differential equations, Prentice-Hall, Englewood Cliffs, N. J., 1963. MR 29 #2672. MR 0165388 (29:2672)
  • [5] I. M. Gel'fand and N. Ja. Vilenkin, Generalized functions, Vol. 4: Some applications of harmonic analysis, Fizmatgiz, Moscow, 1961; English transl., Academic Press, New York, 1964. MR 26 #4173; MR 30 #4152. MR 0435834 (55:8786d)
  • [6] T. Hida, Canonical representations of Gaussian processes and their applications, Mem. Coll. Sci. Univ. Kyoto Ser. A Math. 33 (1960/61), 109-155. MR 22 #10012. MR 0119246 (22:10012)
  • [7] K. Itô, On stochastic differential equations, Mem. Amer. Math. Soc. No. 4 (1951). MR 12, 724. MR 0040618 (12:724a)
  • [8] -, On a formula concerning stochastic differentials, Nagoya Math. J. 3 (1951), 55-65. MR 13 #363. MR 0044063 (13:363g)
  • [9] K. Itô and M. Nisio, On stationary solutions of a stochastic differential equation, J. Math. Kyoto Univ. 4 (1964), 1-75. MR 31 #1719. MR 0177456 (31:1719)
  • [10] M. Jirina, Conditional probabilities on strictly separable $ \sigma $-algebras, Czechoslovak Math. J. 4(79) (1954), 372-380. (Russian) MR 16, 1034. MR 0069416 (16:1034j)
  • [11] P. Lévy, Random functions: General theory with special reference to Laplacian random functions, Univ. California Publ. Statist. 1 (1953), 331-390. MR 14, 1099. MR 0055607 (14:1099f)
  • [12] J. L. Lions, Les semigroupes distributions, Portugal. Math. 19 (1960), 141-164. MR 26 #611. MR 0143045 (26:611)
  • [13] P. A. Meyer, Intégrales stochastiques. I, II, Séminaire de Probabilités (Univ. Strasbourg, 1966/67); vol. I, Springer, Berlin, 1967, pp. 72-117. MR 37 #7000. MR 0231445 (37:7000)
  • [14] Ju. V. Prohorov, The method of characteristic functionals, Proc. Fourth Berkeley Sympos. Math. Stat. and Prob., vol. II (1960), Univ. of California Press, Berkeley, Calif., 1961. MR 24 #A3670. MR 0133846 (24:A3670)
  • [15] L. Schwartz, Sur l'impossibilité de la multiplication des distributions, C. R. Acad. Sci. Paris 239 (1954), 847-848. MR 16, 265. MR 0064324 (16:265e)
  • [16] -, Théorie des distributions, Publ. Inst. Math. Univ. Strasbourg, nos. 9, 10, Hermann, Paris, 1966. MR 35 #730.
  • [17] -, Radon measures on general topological spaces, Tata Institute of Fundamental Research, (to appear).
  • [18] A. V. Skorohod, Studies in the theory of random processes, Iydat Kiev. Univ., Kiev, 1961; English transl., Addison-Wesley, Reading, Mass., 1965. MR 32 #3082a,b. MR 0185620 (32:3082b)
  • [19] J. L. Strand, Generalized stochastic ordinary differential equations, Notices Amer. Math. Soc. 15 (1968), Abstract #654-21, p. 342.
  • [20] F. Treves, Topological vector spaces, distributions and kernels, Academic Press, New York, 1967. MR 37 #726. MR 0225131 (37:726)
  • [21] K. Urbanik, Generalized stationary processes of Markovian character, Studia Math. 21 (1961/62), 261-282. MR 27 #821. MR 0150835 (27:821)
  • [22] K. Yosida, Functional analysis, Die Grundlehren der math. Wissenschaften, Band 123, Academic Press, New York and Springer-Verlag, Berlin, 1965. MR 31 #5054. MR 0180824 (31:5054)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 60.75

Retrieve articles in all journals with MSC: 60.75


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1970-0261719-4
Article copyright: © Copyright 1970 American Mathematical Society

American Mathematical Society