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Results tagged with gaussian-process
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user 207276
Gaussian processes refer to stochastic processes whose realization consists of normally distributed random variables, with the additional property that any finite collection of these random variables have a multivariate normal distribution. The machinery of Gaussian processes can be employed in regression and classification problems.
1
vote
Accepted
Power transformation of OU process
It can be shown that (by using Itô's lemma on $X_t e^{\phi t}$):
$$X_t = X_0e^{-\phi t} + \mu (1 - e^{-\phi t}) + \int_0^t \sigma e^{\phi (t-s)} dW_s $$
Which leads to:
$$\gamma X_t = \gamma X_0e^{-\ …
- 698
3
votes
Accepted
Compute $P\left(\int_0^1W(t)dt>\frac{2}{\sqrt3}\right)$ where $W(t)$ is a Wiener process
$\int_0^1 W_s ds$ is indeed gaussian with mean 0, but to arrive to this conclusion and get its variance the easiest way is to write it as a Wiener integral, i.e: $\int_0^1 ... dW_s$.
As a matter of f …
- 698