ISSN:
1432-0606
Keywords:
Key words. Two-dimensional polymer measure, Closability, Dirichlet forms, Diffusion processes, Ergodicity, Quasi-invariance. AMS Classification. Primary 60J65, Secondary 60H30.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract. We prove that there exists a diffusion process whose invariant measure is the two-dimensional polymer measure ν g . The diffusion is constructed by means of the theory of Dirichlet forms on infinite-dimensional state spaces. We prove the closability of the appropriate pre-Dirichlet form which is of gradient type, using a general closability result by two of the authors. This result does not require an integration by parts formula (which does not hold for the two-dimensional polymer measure ν g ) but requires the quasi-invariance of ν g along a basis of vectors in the classical Cameron—Martin space such that the Radon—Nikodym derivatives (have versions which) form a continuous process. We also show the Dirichlet form to be irreducible or equivalently that the diffusion process is ergodic under time translations.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002459900129
