Abstract
Explicit filtration formulas are obtained for the solutions of nonlinear differential equations with random right-hand sides. In the case of a Gaussian random process, these formulas are simplified.
Similar content being viewed by others
References
R. Sh. Liptser and A. N. Shiryaev,Statistics of Random Processes [in Russian], Nauka, Moscow (1974).
Yu. L. Daletskii and A. D. Shatashvili, “On the optimal prediction of random variables nonlinearly related to the Gaussian random variables,”Teor. Sluch. Prots., Issue 3, 30–33 (1975).
G. A. Sokhadze, “Equivalence of measures corresponding to solutions of certain boundary-value problems with random Gaussian perturbations,”Teor. Ver. Mat. Statist., Issue 39, 116–123 (1988).
G. A. Sokhadze, “Absolute continuity of measures generated with nonlinear equations,” in:New Trends in Probability and Statistics. Proceedings of Bakuriani Colloquium in Honour of Yu. V. Prohorov, Vol. 1, Bakuriani (1990), pp. 540–549.
C. Miranda,Equazioni Alle Derivate Paniali di Tipo Ellittico, Springer, Berlin (1955).
Yu. M. Berezanskii,Expansion of Self-Adjoint Operators in Eigenfunctions [in Russian], Naukova Dumka, Kiev (1968).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 5, pp. 586–596, May, 1994.
Rights and permissions
About this article
Cite this article
Sokhadze, G.A. Filtration formulas for solutions of nonlinear equations with random right-hand sides. Ukr Math J 46, 625–637 (1994). https://doi.org/10.1007/BF01058524
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01058524