Prove that for any (lambda>0), [left(L_{lambda^{2} t}^{x} ; x, t geq 0 ight) stackrel{text { law }}{=}left(lambda

Prove that for any \(\lambda>0\),

\[\left(L_{\lambda^{2} t}^{x} ; x, t \geq 0\right) \stackrel{\text { law }}{=}\left(\lambda L_{t}^{x / \lambda} ; x, t \geq 0\right) .\]

In particular, the following equality in law holds true \[\left(L_{\lambda^{2} t}^{0}, t \geq 0\right) \stackrel{\text { law }}{=}\left(\lambda L_{t}^{0}, t \geq 0\right) .\]