All Questions
7 questions
3
votes
2
answers
325
views
Ito Diffusions with low regularity?
I would like to have an Itô Diffusion
$$ X_t = \int_0^t b(s) \mathrm{d}s + \int_0^t \sigma(s) \mathrm{d}B_s.$$
where the (vector- and matrix-valued, respectively) functions $b$ and $\sigma$ have lower ...
- 9,853
3
votes
0
answers
68
views
Brownian motion on a $\mathbb{Z}$-cover
Let $(M,g)$ a smooth closed Riemannian manifold with non trivial first homology group $H^1(M,\mathbb{R})$. Any element of $H^1(M,\mathbb{Z})$ will define a riemannian $\mathbb{Z}$-cover of $M$ ...
user50806
2
votes
1
answer
221
views
Is there Brownian motion on Alexandrov spaces?
It is well known that there is a notion of Brownian motion on smooth Riemannian manifolds.
I am wondering if there is a more general notion of Brownian motion on finite dimensional Alexandrov ...
- 21.8k
2
votes
0
answers
101
views
The Itō isometry for Riemannian manifolds
If $\alpha$ is a real smooth $1$-form, and if $\mathcal C$ is the space of continuous functions $c : [0,1] \to \mathbb R^n$, endowed with the Wiener measure $w$, and if $I_\alpha : \mathcal C \to \...
- 5,407
2
votes
0
answers
56
views
What is the Wiener measure of the set of curves with given Hölder constant on a Riemannian manifold?
Let $M$ be a connected Riemannian manifold and $x_0 \in M$. For $0 < \alpha < \frac 1 2$, let
$$H = \{ c : [0,1] \to M \mid c(0) = x_0 \text{ and } \exists C>0 \text { s.t. } d(c(s), c(t)) \...
- 5,407
1
vote
0
answers
44
views
What do we know about Poisson boundaries of arbitrary Riemannian manifolds?
For closed manifolds, we know that the Poisson boundary is trivial due to compactness and for radially symmetric manifolds for which diffusion is one dimensional, there are A Brief Introduction to ...
- 168
0
votes
0
answers
88
views
Independent increments for the Brownian motion on a Riemannian manifold
In am not a probabilist, but I must do some stochastic-flavoured work on a connected Riemannian manifold $M$. A nice thing about the Brownian motion on $\mathbb R^n$ is that we may talk about its ...
- 5,407