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4
votes
3answers
186 views

Why is Brownian motion merely 'almost surely' continuous?

Why is Brownian motion required to be merely almost surely continuous instead of continuous? For example, this is stated as condition 2 in this article in section 1, Characterizations of the Wiener ...
7
votes
1answer
272 views

Distribution of Geometric Brownian Motion

Please let me know where I have been mistaken! Let the SDE satisfied by the GBM $S(t)$ be $$ \frac{dS(t)}{S(t)} = \mu dt + \sigma dW(t). $$ Then, the underlying BM $X(t)$ will satisfy $$ dX(t) = ...
3
votes
0answers
88 views

Particular Conditional Expectation of Geometric Brownian Motion

If we have the density function $$f_{Y}(y,t)=\frac{1}{y \sqrt {2\pi\sigma^2t}}exp(-\frac{(ln \ y - \mu t)^2}{2\sigma^2t})$$ Then the mean of $Y(t)=e^{X(t)}$ conditional on $Y(0)=y_0$ is found to be ...
3
votes
0answers
98 views

Estimating two normal random numbers with one equation

Subtitle: Estimating the correlation of the shocks driving two commodities in two multi-factor models I am fitting two 2-factor models to electricity and gas futures, respectively. In order to ...
2
votes
0answers
34 views

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 ...
2
votes
0answers
156 views

How do I artificially generate intraday ticks data from a given input (Open,High,Low,Close,Volume) using Brownian Bridge method?

How do I artificially generate intraday ticks data from a given input (Open,High,Low,Close,Volume) using Brownian Bridge method? https://en.wikipedia.org/wiki/Brownian_bridge P.S: Brownian Bridge ...
1
vote
0answers
26 views

Convolution of inverse gaussian and power law distributions

I am trying to understand how the first passage time density of Brownian motion with drift is modified by the presence of waiting times that are distributed as a power law In other words, what is the ...
1
vote
0answers
114 views

Distribution of Brownian Bridge

I know from Karatzas & Shreve (1991) that a Brownian Bridge $B(t)$ from $a$ to $b$ on time interval $[0,T]$ satisfies: $B(t)=a(1-t/T) + b*t/T + [W(t) - W(T)*t/T]$, where $W(t)$ is a standard ...
0
votes
0answers
11 views

Simulated Price Data via Harmonic Logarithmic Walks?

Hi I came up with this equation last week and was wondering if: 1) There was already a name for this mathematical process. If so, where I might find more information. 2) Also, I am not adept at ...