# Tagged Questions

**1**

vote

**1**answer

172 views

### A stronger version of supramenability?

A group $G$ is supramenable iff for all $\varnothing\ne A\subseteq G$ there is a finitely-additive left-$G$-invariant measure $\mu_A$ on $G$ with $\mu_A(A)=1$. I'm interested in a seemingly stronger ...

**1**

vote

**1**answer

96 views

### Nonstandard definition for the generator of a standard Ito diffusion

For a standard Brownian motion, the generator of the diffusion is
$$
L = \frac12 \frac{d^2}{dx^2}.
$$
Is there a nonstandard definition of this generator?

**5**

votes

**0**answers

134 views

### Constructing black noise with non-standard analysis

With noise in the sense of i.i.d. random sequence,
a noise is black if it is not isomorphic to standard Gaussian white noise.
Tsirelson showed the existence of black noise through the scaling limit ...

**7**

votes

**2**answers

318 views

### Hyperreal finitely-additive measure on [0,1) assigning $b-a$ to $[a,b)$ or $(a,b]$ and infinitesimals to singletons

Is there a hyperreal-valued finitely additive measure on all the subsets of [0,1), or at least the Borel ones, that
assigns $b-a$ to $[a,b)$ and to $(a,b]$ for all $a\lt b,$ and
assigns an ...

**19**

votes

**4**answers

2k views

### Nonstandard analysis in probability theory

I am quite new at nonstandard analysis, and recently I became aware of its use in probability theory mainly through the following two books:
Nelson (1987). Radically Elementary Probability Theory
...