Asymptotic behaviour of solutions
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 ). 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.
KeywordsInvariant Measure Absolute Continuity Exponential Convergence Previous Chapter Stochastic Problem
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