Standard resistance form on the infinite Sierpinski gasket and its trace onto the half-line $[0,\mathrm{\infty })$

We construct a compatible sequence of resistance forms on the graphs approximating the infinite Sierpinski gasket and show that the resistance form given by the limit of the compatible sequence induces the Dirichlet form associated with the Brownian motion on the infinite Sierpinski gasket. Moreover, using this characterization of the Dirichlet form, we obtain an explicit expression of the jump kernel associated with the trace process of the Brownian motion onto the half-line $[0,\mathrm{\infty })$.