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Results tagged with pr.probability
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user 51335
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
0
votes
1
answer
112
views
Ball in separable Banach space has positive Gaussian measure
I have (presumably non-degenerate) Gaussian $\mu$ over separable Banach space $X$. I would like to prove that for any ball of radius $r$ centered at $x$, $\mu(B_r(x))$. I know how to prove this in th …
- 379
1
vote
1
answer
147
views
Conditional Gaussians in infinite dimensions
I asked this over on cross validated, but thought it might also get an answer here:
The law of the conditional Gaussian distribution (the mean and covariance) are frequently mentioned to extend to the …
- 379
1
vote
0
answers
57
views
Choice of Banach space for stochastic processes
In studying $X$ (Banach space) valued stochastic processes, I tend to see two different norms used:
$$
\sup_{t\leq T} \mathbb{E}[\|u(t)\|_{X}^p]^{1/p}
$$
and
$$
\mathbb{E}[\sup_{t\leq T} \|u(t)\|_X^p] …
- 379
2
votes
1
answer
283
views
Sufficient conditions to be a covariance
Given a function, $c(x,y):\mathbb{R}\times \mathbb{R}\to \mathbb{R}$, what are sufficient conditions for this to be the covariance of some (centered) Gaussian random field $X:\mathbb{R}\to \mathbb{R}$ …
- 379
2
votes
1
answer
732
views
Properties of Cameron Martin Space
In the case that I'm working with a separable Hilbert space, $H$, on which I have a trace class operator, $K$, that's coming from a Gaussian (i.e., $K$ is self-adjoint, and for simplicity, has trivial …
- 379
5
votes
2
answers
909
views
Analytic Solution to SDEs
Are there any example of SDEs with constant diffusion terms, other than the Ornstein Uhlenbeck process, which have exact solutions? I'm thinking of something of the form:
\begin{equation}
dX_t = f(X_ …
- 379