Scaling limit of stretched Brownian chains

We show that a properly scaled stretched long Brownian chain converges to a two-parametric stochastic process, given by the sum of an explicit deterministic continuous function and the solution of the stochastic heat equation with zero boundary conditions.

Automated summary

This study demonstrates that a properly scaled stretched long Brownian chain converges to a two-parametric stochastic process, which is the sum of an explicit deterministic continuous function and the solution of the stochastic heat equation with zero boundary conditions.