Donsker’s theorem in Wasserstein-1 distance
Copyright policy )Donsker’s theorem in Wasserstein-1 distance
We compute the Wassertein-1 (or Kolmogorov-Rubinstein) distance between a random walk in $R^d$ and the Brownian motion. The proof is based on a new estimate of the Lipschitz modulus of the solution of the Stein's equation. As an application, we can evaluate the rate of convergence towards the local time at 0 of the Brownian motion.
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Donsker theorem, Strong limit theorems, Stein method, Stochastic calculus of variations and the Malliavin calculus, Malliavin calculus, Probability (math.PR), Gaussian processes, Stein’s method, 510, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 60H07, 60G15, FOS: Mathematics, Stein's method, 60F15, 60G55, Point processes (e.g., Poisson, Cox, Hawkes processes), Wasserstein distance, Mathematics - Probability
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Donsker theorem, Strong limit theorems, Stein method, Stochastic calculus of variations and the Malliavin calculus, Malliavin calculus, Probability (math.PR), Gaussian processes, Stein’s method, 510, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 60H07, 60G15, FOS: Mathematics, Stein's method, 60F15, 60G55, Point processes (e.g., Poisson, Cox, Hawkes processes), Wasserstein distance, Mathematics - Probability
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