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Results tagged with wiener-measure
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user 60556
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Martingale problem for the Wiener process
Consider $\Omega \triangleq \mathbf{C}([0,T];\mathbb{R})$, $\mathbf{F} \triangleq \mathbf{B}(\mathbf{C}[0,T];\mathbb{R})$ (Borelian $\sigma$-algebra) and $\mathbf{F}_t \triangleq \sigma \left \{ W_s, …
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interpretation of the transition probability of a brownian motion in terms of the Wiener mea...
Let $W(t)$ be a standard brownian motion in $E \triangleq \mathbb{R}^d$.
The transition probability from a state $x \in E$ at time $t$ to a state $y \in E$ at time $T$ is
$$
p(x,t;y,T) = \frac{1}{\sq …
- 365