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.
Keywords
- Invariant Measure
- Absolute Continuity
- Exponential Convergence
- Previous Chapter
- Stochastic Problem
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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
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Online ISBN: 978-3-540-45147-1
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