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### Necessary conditions to ensure that stochastic integral is a normal variable

Let $\left(W_t\right)_{t\geq 0}$ be a Brownian motion with respect to filtration $\mathbb{F}=\left(\mathcal{F}_t\right)_{t\geq 0}$. Let $\left(\alpha_t\right)_{t\geq 0}$ be an $\mathbb{F}$-adapted ...
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### Ito Lemma for Poisson Process

I'm new to stochastic calculus on jump processes and encountered a difficulty. I would appreciate some clarification from the community on the following question. Let $g_t$ be a $\mathcal{F_t}$-...
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### Brownian Bridge general case

The SDE for the Brownian bridge is the following: $dY_t=\frac{b-Y(t)}{1-t}dt+dW(t)$ with solution: $Y(t)=Y(0)(1-t)+bt+(1-t)\int_0^t \dfrac{dW(s)}{1-s}$ Can someone help me on proving that \lim_{t\...
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### Solving SDE Dubins-Schwarz Theorem

$\text{ Let } X_{t}=1+t+B_{t}, \text { and } T=\inf \left\{t: X_{t}=0\right\} . \text { Define } G(t)=\int_{0}^{t \wedge T} \frac{d s}{X_{s}}.$ \$\text { Let }\ \tau_{t}=G^{-1}(t) \text { be the ...
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