# Tag Info

### Integral of Brownian motion w.r.t. time

This type of integral has appeared so many times and in so many places; for example, here, here and here. Basically, for each sample $\omega$, we can treat $\int_0^t W_s ds$ as a Riemann integral. ...
Accepted

### Finding distribution of $\int_0 ^T uW_u du$

Using the Ito Formula The general approach that often works for these kinds of question is to search for functions such that their Ito differential contains the terms that we are interested in. In ...
Accepted

### Processes used in quant finance

Here is a short list (to be edited and improved - community wiki) : Standard brownian motion (also called Wiener process) for which: $d\, W_t \sim \mathcal N(0, \sqrt{d t})$ Geometric brownian ...
Accepted

### Why is Brownian motion useful in finance?

Brownian motion is simply the limit of a scaled (discrete-time) random walk and thus a natural candidate to use. It is very intuitive and arguably one of the simplest and best understood time-...
### Difference between $W_t$ and $X_t= \sqrt{t}Z$
The means are equal Suppose $f$ is analytic so that we can give it a Taylor series that works everywhere such that $f(x) = \sum a_n x^n$, and then let us let this be bounded too. To show that the ...