# Questions tagged [brownian-motion]

In mathematics, Brownian motion is described by the Wiener process; a continuous-time stochastic process named in honor of Norbert Wiener.

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### Simulating Stock's close, high and low prices

I am testing a model in which I need to simulate closing, high and low prices (i.e. 3 dimensions of prices) of any given stock. Using the simple Geometric Brownion Motion equation I can easily ...
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### Geometric Brownian Motion and Energy-Efficiency Investments

Suppose the payoff $X$ on an investment follows a Geometric Brownian Motion: $$dX/X = \mu dt + \sigma dz\ ,$$ for $dz$ an increment of a Wiener process. I wish to compute the expected present value ...
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### Are the increments of a stochastic process driven by fractional Brownian motion independent?

I'm studying the following equation $$\tag1 dX_t = \mu X_t dt + \sigma X_t dB^H_t$$ where $B^H$ is the fractional Brownian motion (fBm) of Hurst parameter $H\in(0,1)$, that is a continuous ...
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### Is Geometric Brownian Model suitable for long term price forecast?

I was thinking of using Geometric Brownian Motion to forecast future prices of timber (say one variable, the stumpage price of sawtimber). I tested the time series with Augmented Dickey-Fuller test ...
2answers
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### Is the Brownian motion multiplication rule a definition or is it a theorem?

Is the Brownian motion multiplication rule a definition or is it a theorem? Refer to the highlight part of http://i.stack.imgur.com/doQuT.png where $dw_1(t)dw_1(t)=dt$
3answers
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### Browian motion: $P(B_1<4 | B_2 =1)$

I want to calculate $P(B_1<4 | B_2 =1)$ for the B.M. What I tried: $P(B_1<4 | B_2 =1)=P(B_1 - B_2 < 3- B_2 | B_2 =1)$ but I cant use any independence to calculate further.
2answers
148 views

### 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 ...
4answers
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### Ito Integral of functions of Brownian motion

How does one show that: $$\mathbb{E}\left[ \int f(W_s)dWs \right] = 0$$ For all $f()$ that are powers of $W(s)$?? I assume that one would have to go via the definition of Ito integral and express ...
2answers
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