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Invariant Measures for One Class of Linear Stochastic Systems in Hilbert Spaces

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We establish coefficient conditions for the existence and uniqueness of invariant measures in Hilbert spaces for linear stochastic equations.

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References

  1. G. Da Plato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Cambridge Univ. Press, Cambridge (1992).

  2. G. Da Plato and J. Zabczyk, Ergodicity for Infinite-Dimensional Systems, Cambridge Univ, Press, Cambridge (1996).

  3. N. Kryloff and N. Bogoliouboff, “La théorie générale de la measure dans son application à l’étude des systèms dynamiques de la mécanique non linéaire,” Ann. Math. (2), 38, No. 1, 65–113 (1937).

    Article  MathSciNet  Google Scholar 

  4. V. I. Bogachev and M. Rockner, “Elliptic equations for measures on infinite-dimensional spaces and applications,” Probab. Theory Related Fields, 120 (4), 445–496 (2001).

    Article  MathSciNet  Google Scholar 

  5. G. Mueller, “Coupling and invariant measures for the heat equation with noise,” Ann. Probab., 21(4), 2189–2199 (1993).

    Article  MathSciNet  Google Scholar 

  6. S. Assing and R. Manthey, “Invariant measures for stochastic heat equations with unbounded coefficients,” Stoch. Proc. Appl., 103(2), 237–256 (2003).

    Article  MathSciNet  Google Scholar 

  7. S. Cerrai, “Stochastic reaction diffusion system with multiplicative noise and non-Lipschitz reaction term,” Probab. Theory Related Fields, 125(2), 271–304 (2003).

    Article  MathSciNet  Google Scholar 

  8. O. Misiats, O. Stanzhytskyi, and N. K. Yip, “Existence and uniqueness of invariant measures for stochastic reaction-diffusion equations in unbounded domains,” J. Theor. Probab., 29(3), 996–1026 (2015).

    Article  MathSciNet  Google Scholar 

  9. O. Misiats, O. Stanzhytskyi, and N. K. Yip, “Asymptotic analysis and homogenization of invariant measures,” Stochast. Dyn., 19, No. 2, 1950015 (2019).

    Article  MathSciNet  Google Scholar 

  10. O. Misiats, O. Stanzhytskyi, and N. K. Yip, “Invariant measures for stochastic reaction-diffusion equation with weakly dissipative nonlinearities,” Stochastics (2019); https://doi.org/10.1080/17442508.2019.1691212.

  11. D. Henry, Geometric Theory of Semilinear Parabolic Equations, Springer, Berlin (1981).

    Book  Google Scholar 

  12. E. C. Titchmarsh, Eigenfunction Expansions Associated with Second-Order Differential Equations, Clarendon Press, Oxford (1958).

    Book  Google Scholar 

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Correspondence to I. H. Novak.

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Translated from Neliniini Kolyvannya, Vol. 22, No. 4, pp. 519–525, October–December, 2019.

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Novak, I.H., Stanzhytskyi, A.O. Invariant Measures for One Class of Linear Stochastic Systems in Hilbert Spaces. J Math Sci 254, 271–279 (2021). https://doi.org/10.1007/s10958-021-05303-8

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  • DOI: https://doi.org/10.1007/s10958-021-05303-8

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