- #1
mnb96
- 715
- 5
Hello,
when we have a deterministic signal f:ℝ→ℝ that is square integrable we can typically write [itex]f \in L^2(\mathbb{R})[/itex].
However, what if [itex]\{ f(t): \; t\in \mathbb{R} \}[/itex] are random variables, i.e. f is a continuous-time stochastic process?
What is the notation to denote the space of "square integrable" stochastic processes?
Here for square integrable I mean the following:
[tex]E\left\{ \int_{-\infty}^{+\infty} |f(t)|^2 dt \right\} < \infty[/tex]
where E denotes the expected value.
when we have a deterministic signal f:ℝ→ℝ that is square integrable we can typically write [itex]f \in L^2(\mathbb{R})[/itex].
However, what if [itex]\{ f(t): \; t\in \mathbb{R} \}[/itex] are random variables, i.e. f is a continuous-time stochastic process?
What is the notation to denote the space of "square integrable" stochastic processes?
Here for square integrable I mean the following:
[tex]E\left\{ \int_{-\infty}^{+\infty} |f(t)|^2 dt \right\} < \infty[/tex]
where E denotes the expected value.