Asymptotic behaviour of solutions

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


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.


Invariant Measure Absolute Continuity Exponential Convergence Previous Chapter Stochastic Problem 
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© Springer-Verlag Berlin Heidelberg 2001

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