# Questions tagged [brownian]

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### How to prove that the following is still a Brownian motion [closed]

Given a Brownian motion $B_t$ on a filtered probability space, how can I prove that $W_t=B_t+\alpha t$ is still a Brownian motion, with $\alpha \in \mathbb{R}$? Is it always true? Do I need necessarly ...
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### Proof: Brownian Motion Path Continious with Probability One [closed]

How can one show that the paths of the standard Wiener process are continuous in $T$ with probability one? Can we just proof it with the assumption of independence ? Thank You in advance!
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### Itos Lemma Derivation notation

So in Hull (2012) the main point is that $\Delta x^2 = b^2 \epsilon ^2 \Delta t +$higher order terms has a term of order $\Delta t$ and can not be ignored as the Brownian motion exhibits the ...
### Ito formula for $Y_t=tB_t$
someone can help me to solve this problem: $B_t$ is a Standard Brownian Motion. Let $Y_t=tB_t$. Using Ito formula, find drift and volatility of $Y_t$. The result I found is $dY_t=B_tdt+t\cdot dB_t$ ...
Have a question about "How to estimate parameters for SDE with multiple Brownian Motions ?" Let's say $X_t$ follows the process: $dX_t=\mu dt+\sigma_1 dW_t^1 + \sigma_2 dW_t^2$ I think I've checked ...