Given a (standard) Brownian Motion $W_t$ if we do some sort of scaling, inversion or reversal then we also get a Brownian motion.
I have seen proofs but the proofs only seem to rely on showing covariance is the minimum of two given (arbitrary) times and the continuity.
I can't seem to find a theorem or lemma in my book that states this is all that needs to be checked rather than entirely check the 4 parts of the definition of Brownian motion.
Could someone either state or give reference (which I can find online) to this? That is much simpler than having to prove by the definition.