Questions tagged [wiener]
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4
questions
4
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496 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 $B_t = W_t^3 - 3tW_t$. ...
4
votes
2answers
802 views
Reflection Principle
Let $(\Omega,\mathcal{F},P)$ be a probability space and $\{W_t ∶ t ≥ 0\}$ be a standard
Wiener process. By setting $\tau$ as a stopping time and defining
\begin{align}
W^*(t)=\Big\{\matrix{W_t\,\,\,\,...
4
votes
2answers
619 views
Integration on Wiener Process
How can I show that below equation holds ?
$\int\limits_{0}^{t} f \left( s \right)W_s ds = W_t \int\limits_{0}^{t}f \left( s \right)ds - \int\limits_{0}^{t}\int\limits_{0}^{s} f\left( u \right)dudW_s $...
3
votes
1answer
413 views
Discretization of Wiener process
The Wiener process $(W_t)$ is a continuous stochastic process that satisfies the following there conditions:
$W_0 = 0$,
the increments $\mathrm{d}W_t = W_{t + \mathrm{d}t} - W_t$ are normally ...
