Abstract
We are still concerned with the stochastic evolution equation
where b : [0, T] × ℝd → ℝd and σ : [0, T] σ ℝd → L(ℝr; ℝd) fulfill Hypothesis 8.1 whereas B is an r-dimensional Brownian motion in a probability space (Ω, ℱ, ℙ) (we shall denote by (ℱ t ) t ≥ 0 its natural filtration). By Theorem 8.2 we know that problem (9.1) has a unique solution X (·, s, x).
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© 2014 Scuola Normale Superiore Pisa
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Da Prato, G. (2014). Relationship between stochastic and parabolic equations. In: Introduction to Stochastic Analysis and Malliavin Calculus. Publications of the Scuola Normale Superiore, vol 13. Edizioni della Normale, Pisa. https://doi.org/10.1007/978-88-7642-499-1_9
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DOI: https://doi.org/10.1007/978-88-7642-499-1_9
Publisher Name: Edizioni della Normale, Pisa
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