5
votes
1answer
335 views

$\int_0^tB_s^2\ dB_s$ - Gaussian Process and independent increments?

For $(B_t)_{t\ge0}$ a standard Brownian motion (Wiener process) define the stochastic process $X_t:=\int_0^tB_s^2\ dB_s$. I am currently trying to assess if $(X_t)_{t\ge0}$ is a Gaussian process and ...
2
votes
1answer
123 views

Weighted integral of random variables

Given a random zero-mean gaussian random variable $X(t)$ with parameter $t$, such that $E [X(t) X(t^\prime)] = \sigma^2 (t) \delta_{tt^\prime}$, is it possible to produce a single gaussian random ...
1
vote
3answers
176 views

Computing Some Integrals via Gauss Integral

$ \displaystyle\int_{-\infty }^\infty e^{-\frac{1}{2} x^2} \; dx $ and $ \displaystyle\int_{-\infty }^\infty x^{2}e^{-\frac{1}{2}x^2} \; dx $ how i compute these integrals via Gauss Integral?