Stationarity of the Solution for the Semilinear Stochastic Integral Equation on the Whole Real Line

  • Bijan Z. ZangenehEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 34)


In this article we prove the stationarity of the solution of the H-valued integral equation
$$X(t) =\displaystyle\int _{ -\infty }^{t}U(t - s)f(X(s))\mathrm{d}s + V (t),$$
where H is a real separable Hilbert space. In this equation, U(t) is a semigroup generated by a strictly negative definite, self-adjoint unbounded operator A, such that A  − 1 is compact and f is of monotone type and is bounded by a polynomial and V (t) is a cadlag adapted stationary process.


Integral Equation Mild Solution Separable Hilbert Space Energy Inequality Galerkin Approximation 
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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Mathematical SciencesSharif University of TechnologyTehranIran

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