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6 votes
0 answers
88 views

Error estimates for projection onto the Wiener chaos expansion for stochastic Sobolev spaces (stochastic Rellich–Kondrachov theorem)

Let $n$ be a positive integer, $s\in \mathbb{R}$, $(\Omega,\mathcal{F},(\mathcal{F}_t)_{t\ge 0},\mathbb{P})$ be a filtered probability space whose filtration supports and is generated by an $n$-...
ABIM's user avatar
  • 5,405
4 votes
1 answer
143 views

When does an Itô diffusion give a semigroup on $L^2$

I would like a reference for when an Itô diffusion generates a strongly continuous semigroup on $L^2(\mathbb{R}^n)$. I have a time-homogeneous Itô diffusion of the form $$dX_t=b(X_t)dt+\sigma(X_t)dB_t$...
SnowRabbit's user avatar
2 votes
0 answers
413 views

On the infinitesimal generator of a 1-dimensional stochastic heat equation: core and explicit form

Denote $E = C([0, 1])$. I am consider a 1-dimensional stochastic heat equation on $h$: $$\partial_tu(t, x) = \partial_x^2u(t, x) - V'(u(t, x)) + \dot{W}(t, x), \quad\text{ for all } (t, x) \in (0, \...
gregarki khayal's user avatar
1 vote
0 answers
95 views

Generator of a Hilbert space valued Wiener process from the solution of a martingale problem

Let $H$ be a separable $\mathbb R$-Hilbert space, $Q\in\mathfrak L(U)$ be nonnegative and self-adjoint with $\operatorname{tr}Q<\infty$ and $(W_t)_{t\ge0}$ be a $H$-valued Wiener process on a ...
0xbadf00d's user avatar
  • 167