Existence Results for Some Partial Stochastic Differential Equations

Paul H. Bezandry () and Toka Diagana ()
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Paul H. Bezandry: Howard University, Department of Mathematics
Toka Diagana: Howard University, Department of Mathematics

Chapter Chapter 6 in Almost Periodic Stochastic Processes, 2011, pp 143-195 from Springer

Abstract: Abstract Chapter 6 deals with the existence of p-th mean almost periodic mild solutions for some classes of stochastic partial evolution equations with infinite delay of type $$\begin{array}{lll}d[X(\omega, t) + f_1(t, X_t, (\omega))] & = & \left[\mathcal{A}X(\omega, t) + f_2(t, X_t(\omega))\right]dt \\ {} & + & f_3(t, X_t(\omega))d \mathbb{W}(\omega, t), \ t \in \mathbb{R}, \ \omega \in \Omega ,\end{array}$$ where $$\mathcal{A} : \mathcal{D} = \mathcal{D}(\mathcal{A})\subset \mathbb{H} \to \mathbb{H}$$ is a sectorial linear operator whose corresponding analytic semigroup is hyperbolic, that is, $$\sigma (\mathcal{A})\cap i\mathbb{R}$$ is empty, and $$f_1 : \mathbb{R} \times \mathbb{H} \to \mathbb{H}_{\beta} (0

Keywords: Banach Space; Periodic Solution; Existence Result; Mild Solution; Analytic Semigroup (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-1-4419-9476-9_6

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