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Results tagged with pr.probability
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user 40502
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
2
votes
1
answer
110
views
Question about infinite-dimensional BM
Suppose we are given an $L^2(\mathcal{D})$-valued Brownian motion $W_t$ defined by
$$W_t:=\sum_{k=1}^{\infty}\sqrt{\sigma_k}W_t^k\phi_k(x),$$
where $\mathcal{D}$ is bounded domain in $\mathbb{R}^d$, $ …
- 121
10
votes
2
answers
995
views
Does the strong law of Large Number hold for an infinite dimensional Brownian motion?
For finite-dimensional Brownian motion $W_t$, it is well known that
\begin{equation}
\lim_{t\to \infty}\frac{W_t}{t}=0,\text{ a.s. }\ \ \ \ \hspace{1cm} \langle 1\rangle
\end{equation}
Now suppose we …
- 121