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can I integrate product or square of a white noise in any sense?

Assume that we have $\epsilon_1, \; \epsilon_2$ independent white noises. Can I write $\int_{0}^1 \epsilon_1^2(t)dt$ Can I write $\int_{0}^1 \epsilon_1(t) \epsilon_2(t)dt$ 1 and 2 obviously make no ...
Sergiusz Wesolowski's user avatar