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Results tagged with wienerprocess
Search options questions only
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user 7788
4
votes
3
answers
2k
views
Determine $E[W_p W_q W_r]$
Given prob space $(\Omega, \mathscr{F}, P)$ and a Wiener process $(W_t)_{t \geq 0}$, define filtration $\mathscr{F}_t = \sigma(W_u : u \leq t)$
Let 0 < p < q < r. Determine $E[W_p W_q W_r]$.
My atte …
- 935
4
votes
3
answers
598
views
Show that $E[B_t|\mathscr{F}_s] = B_s$ for $B_t = W_t^3 - 3 t W_t$
Given prob space $(\Omega, \mathscr{F}, P)$ and a Wiener process $(W_t)_{t \geq 0}$, define filtration $\mathscr{F}_t = \sigma(W_u : u \leq t)$
Let $(B_t)_{t \geq 0}$ where $B_t = W_t^3 - 3tW_t$. Sho …
- 935
4
votes
2
answers
840
views
Solving a backwards heat equation using stochastic calculus
Given the PDE
$$\frac{\partial F}{\partial t} + \frac{1}{2}\sigma^2 \frac{\partial^2 F}{\partial x^2} = 0$$
with condition $F(T,x) = x^2$, one can use the Feynman-Kac formula to arrive at
$$F(t,x) …
- 935