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Results tagged with fa.functional-analysis
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user 46900
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
2
votes
0
answers
166
views
Must rows of a transition matrix be distinct?
Is it true that for all continuous time Markov processes on a countable state space $S$, we have
all rows of the transition matrix $\mathbf{P}_t$ are distinct for all time $t\in[0,\infty)$ ?
This i …
- 165
3
votes
0
answers
113
views
Stationarity of Brownian motion with drift
Suppose the following SDE for $X_t$ is well-posed:
$$dX_t = \sqrt{2}\, dB_t - \nabla\Phi(X_t)\,dt.$$
For what $\Phi\in C^1(R^d)$ will $X$ have stationary distribution $u_{\infty}$? For what $\Phi$ w …
- 165
0
votes
1
answer
603
views
Is this Holder-type inequality true $\;(\int fg )\,(\int f^2 + g^2)\leq \int f^2g+fg^2\;$? [closed]
Suppose $f$ and $g$ are non-negative functions such that $\int f(x)dx = \int g(x)dx=1$. Is it true that
$$\Big(\int fg \Big)\,\Big(\int f^2 + g^2\Big)\leq \int f^2g+fg^2\quad?$$
- 165