Rate of convergence of the conditioned random walk towards the Brownian bridge

Key Points

• The conditioned random walk converges towards the brownian bridge, showing promising results in terms of distance metrics.
• The fortet-mourier distance between conditioned processes and the brownian bridge is bounded effectively, supporting convergence claims.
• Combining a functional stein method with radon-nikodym representation aids in establishing rigorous bounds for the convergence.
• Findings suggest a strong relationship between discrete random walks and continuous processes, indicating potential applications in probability theory.

Abstract