# Tagged Questions

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### How to model a stochastic process, continuous in stepsize, which converges against a simple random walk?

I want to compute the probability distribution for a stochastic process with discrete number of steps, where each real value has a nonvanishing probability to be the next stepsize. And I want to ...
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### Form of the spectral density in Wiener Khinchin theorem?

The Wiener–Khinchin theorem says the autocorrelation function of a wide sense stationary process can be written as a Stieltjes integral, where the integrator function is called the power spectral ...
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### Power spectrum for discrete signals.

If $x(t)$ is a real (aperiodic) power signal, i.e. $$0<\lim_{T\rightarrow\infty} \frac{1}{T}\int_{-T/2}^{T/2}|x(t)|^2 dt<\infty$$ $x_T (t)$ is a truncated version of ...
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### Why is the Fourier Transform of a Lévy Process a continuous function? What about the inverse? (Bochners Theorem)

I was confronted with this question when reading "Stochastic Integration and Differential Equations" by Protter. Just after the definition of a Lévy process he says the following: If $X_t$ is a ...
If I have a discrete time series $x(t_i)$, and each of the $x(t_{i})$ are normally distributed, i.e., come from a Gaussian distribution with mean zero and variance one, would a windowed finite Fourier ...