# Tagged Questions

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### Expectation of a Poisson Process

Cars pass a certain street location according to a Poisson Process with rate $\lambda$. An old lady and her trusty boyscout want to cross the street at this location. They wait until they can ensure ...
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### How to calculate this easy stochastic integral?

I have a relatively simple homework for stochastic calculus that I recently started to learn. I cannot seem to calculate the following integral: $$\int_0^t s dW_s$$ In principle, it should be solved ...
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### Why is this a martingale?

In our homework assignment, we are supposed to prove: If $M$ is a countinuous local martingale and if for each $T > 0, E[\sup_{t \leq T } |M_t|] < + \infty$ and $H^T$ is a bounded ...
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### Is this local martingale a true martingale?

Using the Ito's formula I have shown that $X_t$ is a local martingale, because $dX_t=\dots dB_t$, where $$X_t = (B_t+t)\exp\left(-B_t-\frac{t}{2}\right),$$ $B_t$ - is a standard Brownian motion I ...
Let $W_t$ be a Brownian motion with $m$ independent components on $(\Omega,F,P)$. Let $G(\omega,t)=[g_{ij}(\omega,t)]_{1\leq i\leq n,1\leq j\leq m}$ in $V^{n\times m}[S,T]$ such that ...