On Lp-version of tempered Bohl–Perron theorem for infinite-dimensional random differential equations
Ngo Thi Thanh Nga, Nguyen Thi Phuong Mai, Nguyen Huu Du, Le Anh Tuan · Stochastics · 2024
In this paper, we are concerned with LKp–L1q versions of the tempered Bohl–Perron Theorem for linear differential random dynamical systems over θ on Banach spaces. We prove that a random dynamical system is tempered exponentially stable if and only if for any random process f∈LKp, the solutions of the equation u˙=A(θtω)u+f belong to L1q.