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Weak convergence of $\sigma$-finite measures
Let $(E,\mathcal{E})$ be a measure space and let $(m_{n})_{n\in\mathbb{N}} \subset \mathcal{M}_\sigma(E,\mathcal{E})$ be a sequence of $\sigma$-finite measures. I will put my questions and state below …
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On the existence and uniqueness of solution to SPDE with nonlinear growth coefficients
Call the drift term $b(u) = u (K- u)$ and for simplicity set $K=1$. Consider the following space of functions:
$$C_{\text{tem}}(\mathbb{R},\mathbb{R}) = \{ f:\mathbb{R} \to \mathbb{R}:\, \sup_{x \in \ …