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arXiv · 1707.08723

Bohr/Levitan Almost Periodic and Almost Automorphic Solutions of Linear Stochastic Differential Equations without Favard's Separation Condition

David Cheban
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Abstract

We prove that the linear stochastic equation $dx(t)=(A(t)x(t)+f(t))dt+g(t)dW(t)$ with linear operator $A(t)$ generating a continuous linear cocycle $\varphi$ and Bohr/Levitan almost periodic or almost automorphic coefficients $(A(t),f(t),g(t))$ admits a unique Bohr/Levitan almost periodic (respectively, almost automorphic) solution in distribution sense if it has at least one precompact solution on $\mathbb R_{+}$ and the linear cocycle $\varphi$ is asymptotically stable.

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David Cheban. 2017-07-27. Bohr/Levitan Almost Periodic and Almost Automorphic Solutions of Linear Stochastic Differential Equations without Favard's Separation Condition. https://arxiv.org/abs/1707.08723

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