A stochastic perturbation of Wright's delay equation with bounded Lipschitz noise admits a trivial invariant measure at -1 and a nontrivial invariant measure supported on (-1, infinity).
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Sufficient conditions are given for invariant probability measures in stochastic delay differential equations driven by integrable Lévy noise, with a key reduction from bounded solutions to bounded segments under a one-sided bound on the deterministic coefficient.
Non-trivial invariant measures exist for stochastic Mackey-Glass and Nicholson's blowflies equations if and only if solutions remain bounded away from zero in probability for at least one initial condition.
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Stochastic Wright's Equation: Existence of Invariant Measures
A stochastic perturbation of Wright's delay equation with bounded Lipschitz noise admits a trivial invariant measure at -1 and a nontrivial invariant measure supported on (-1, infinity).
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Existence of Invariant Probability Measures for Stochastic Differential Equations with Finite Time Delay
Sufficient conditions are given for invariant probability measures in stochastic delay differential equations driven by integrable Lévy noise, with a key reduction from bounded solutions to bounded segments under a one-sided bound on the deterministic coefficient.
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Stochastic Mackey-Glass Equations and Other Negative Feedback Systems: Existence of Invariant Measures
Non-trivial invariant measures exist for stochastic Mackey-Glass and Nicholson's blowflies equations if and only if solutions remain bounded away from zero in probability for at least one initial condition.