Abstract
In the first part of these notes we consider the following class of stochastic differential equations dξ(t) = b(ξ()) dt + σ(ξ())dw(t), ξ(0) = χ∈ℝd, where w(t) = (w 1 (t),... ,W d(t)) is a standard d-dimensional Brownian motion, the vector field b : ℝd → ℝd and the matrix valued function σ : ℝd → ℒ(ℝd) are smooth and have polynomial growth together with their derivatives and b enjoys some dissipativity conditions.
Keywords
- Banach Space
- Invariant Measure
- Stochastic Differential Equation
- Polynomial Growth
- Separable Banach Space
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© 2001 Springer-Verlag Berlin Heidelberg
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(2001). Introduction. 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_1
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DOI: https://doi.org/10.1007/3-540-45147-1_1
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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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