[Merged by Bors] - feat: a sufficient condition for stochastic processes to be independent

[EtienneC30]

We prove that two stochastic processes $(X_s)_{s \in S}$ and $(Y_t)_{t \in T}$ are independent if for all $s_1, ..., s_p \in S$ and $t_1, ..., t_q \in T$ the two families $(X_{s_1}, ..., X_{s_p})$ and $(Y_{t_1}, ..., Y_{t_q})$ are independent. We prove an analogous condition for a family of stochastic processes.

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[github-actions]

PR summary dc82ad56b5

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Probability.Independence.Process (new file)	1665

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Declarations diff

++ IndepFun.indepFun_process
++ iIndepFun.iIndepFun_process

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

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No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[RemyDegenne]

I would replace processes by process in every lemma name and in the file name, since we most often use singular for names (and it's shorter). Apart from that name change, it looks good to me!
bors d+

[mathlib-bors]

✌️ EtienneC30 can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

[EtienneC30]

Thanks!
bors merge

[mathlib-bors]

Pull request successfully merged into master.

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