All Questions

Suppose that $X_t$ is a real-valued stochastic process. Then is $X_t$ characterized by it's conditional moments? In the sence that, if $Y_t$ is another process, such that $$ \mathbb{E}\left[\int_s^T\...

Let $f(x)$ be a positive definite function on $x \in R^d$. Assume $f(x)$ is radial , so $f(x)$ is a function of $|x|$, let's say $g(|x|):=f(x)$. How can I show that $g(|x|^\gamma)$ is positive ...

I am looking for $\delta>0$, such that $$ \delta \int_{-\infty}^{\infty} \exp(its) { \Gamma\{2(it+1)/3\}\over \Gamma\{(it+1)/2\} }dt \le \\ \int_{-\infty}^{\infty} \exp(its) { \Gamma (it+1)\over \...

Suppose $f(x)$ is a probability density on $\mathbb{R}$. Let $\varphi(t)=\int e^{itx}f(x)dx$ denote the Fourier transform (characteristic function). It is well-known that if $\int |x|^p f(x)dx<\...