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== Diffusion Process ==
Let <math>E = \mathbb{R}^d</math> be the state space with Borel <math>\sigma</math>-algebra, and let <math>\Omega = C([0,\infty), \mathbb{R}^d)</math> denote the canonical space of continuous paths. A family of probability measures <math>\mathbb{P}^{\xi,\tau}_{a;b}</math> (for <math>\tau \geq 0</math>, <math>\xi \in \mathbb{R}^d</math>) solves the diffusion problem for coefficients <math>a^{ij}(x,t)</math> (uniformly continuous) and <math>b^i(x,t)</math> (bounded, Borel measurable) if:
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