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Stationary Solutions of Neutral Stochastic Partial Differential Equations with Delays in the Highest-Order Derivatives
In this work, we shall consider the existence and uniqueness of stationary
solutions to stochastic partial functional differential equations with additive
noise in which a neutral type of delay is explicitly presented. We are
especially concerned about those delays appearing in both spatial and temporal
derivative terms in which the coefficient operator under spatial variables may
take the same form as the infinitesimal generator of the equation. We establish
the stationary property of the neutral system under investigation by focusing
on distributed delays. In the end, an illustrative example is analysed to
explain the theory in this work
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