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Asymptotic behaviour of solutions

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Second Order PDE’s in Finite and Infinite Dimension

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1762))

Abstract

We are here concerned with the study of the asymptotic behaviour of the solution of the stochastic equation dξ(t) = b(ξ()) dt + σ(ξ())dw(t), ξ(0) = χ∈ℝd. (2.0.1) If the coefficients b and σ are Lipschitz-continuous, then the problem is well studied (for a bibliography see for example [48]). But here, as in the previous chapter, we are considering coefficients b and a which are only locally Lipschitz. In fact, we assume the following conditions for σ and σ.

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© 2001 Springer-Verlag Berlin Heidelberg

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(2001). Asymptotic behaviour of solutions. In: Cerrai, S. (eds) Second Order PDE’s in Finite and Infinite Dimension. Lecture Notes in Mathematics, vol 1762. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45147-1_3

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  • DOI: https://doi.org/10.1007/3-540-45147-1_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42136-8

  • Online ISBN: 978-3-540-45147-1

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