Skip to main content

All Questions

Filter by
Sorted by
Tagged with
6 votes
1 answer
387 views

Reference Request: Vector-Valued Ito Formula

I know that there exist Ito formulae to understand $ f(X), $ where $f: H\rightarrow \mathbb{R}$ is sufficiently nice, $H$ is a Hilbert space and $X$ is an $H$-valued semi-martingale. However I'm ...
ABIM's user avatar
  • 5,405
1 vote
1 answer
164 views

Hilbert-Space Values SDE in terms of Basis

Suppose: $$ dX_t = a(t,X_t)dt + b(t,X_t)dW^H_t $$ is an SDE with values in a separable Hilbert Space $H$, and $W^H_t$ is an $H$-valued cylindrical Wiener process. Then can we write the dynamics for $...
ABIM's user avatar
  • 5,405
1 vote
1 answer
133 views

Reference for convergence of Hilbert-space valued SDEs

I'm fairly familiar with the literature dealing with convergence of SDEs in $\mathbb{R}^d$ but recently I've needed to use extended results dealing with convergence of SDEs in Hilbert Spaces. However ...
ABIM's user avatar
  • 5,405