Transportation cost inequalities on path and loop groups

摘要

Let G be a connected Lie group with the Lie algebra W. The action of Cameron-Martin space H(zeta) on the path space P-e(G) introduced by L. Gross (Illinois J. Math. 36 (1992) 447) is free. Using this fact, we define the H-distance on P-e(G), which enables us to establish a transportation cost inequality on P-e(G). This method will be generalized to the path space over the loop group L-e(G), so that we obtain a transportation cost inequality for heat measures on L-e(G). (C) 2004 Elsevier Inc. All rights reserved.