Null Controllability for Degenerate Parabolic Operators
Null Controllability for Degenerate Parabolic Operators
Null Controllability for Degenerate Parabolic Operators
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• X(·, x)invariant sets <strong>for</strong> stochastic flowsunique solution{dX(t) = b(X(t))dt + σ(X(t)) dW (t) t ≥ 0X(0) = x ∈ R n• b : R n → R n , σ : R n → L(R n ; R m ) Lipschitz• W (t) m-dimensional Brownian (Ω, F, {F t } t , P)• K ⊂ R n invariantx ∈ K =⇒ X(t, x) ∈ K P − a.s. ∀t ≥ 0✬ K x✩✫✪