20
votes

Accepted

### Is there any reason to use paracontrolled calculus over regularity structures?

I don't think that the reason given in the paper by Bailleul and Bernicot is a good one. Basically, they treat an example which is simple enough so that it is still manageable to describe the various ...

6
votes

Accepted

### Truncated fixed point and regularity structures

Before I try to answer the broader question let me try to clear up a potential confusion. The truncations that appear at the level of modelled distributions don't really change the distribution they ...

2
votes

### How to compare pathwise convergence and convergence in probability

As I did not get any reply, I am trying to verify my understanding. This is related to convergence of SDE/PSDE through Ito type calculous and rough path or regularity structure. Any comments would be ...

1
vote

Accepted

### Do regularity structures involve infinite "Taylor" series?

So one good start is "Rough Stochastic PDEs". Here Hairer builds a notion of an SPDE solution using rough paths
first building the invariant solution $\psi_{t}(x)$ and lifting to a rough ...

1
vote

Accepted

### When and why do we require the condition that :"a subset bounded from below and has no accumulation points?"

From the references mentioned in the comments , (section 4.4,"Renormalisation of parabolic stochastic PDEs") (RP) and (section 6.1,"Introduction to regularity structures") (IRS), ...

1
vote

### Why does the correct scaled dimension for SPDEs count time as two dimensions?

the links on the video and notes are not there. But indeed as they explain in "Stochastic PDEs, Regularity Structures, and Interacting Particle Systems" at page 13, the main reason is that ...

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