scholarly journals Overdamped limit of generalized stochastic Hamiltonian systems for singular interaction potentials

2019 ◽  
Vol 20 (2) ◽  
pp. 577-605
Author(s):  
Martin Grothaus ◽  
Andreas Nonnenmacher
Keyword(s):  
Hamiltonian Systems ◽  
Interaction Potentials ◽  
Singular Interaction ◽  
Stochastic Hamiltonian Systems ◽  
Overdamped Limit

scholarly journals Closability of quadratic forms associated to invariant probability measures of SPDEs

2017 ◽  
Vol 20 (04) ◽  
pp. 1750023
Author(s):  
Michael Röckner ◽  
Feng-Yu Wang
Keyword(s):  
Probability Measure ◽  
Hamiltonian Systems ◽  
General Result ◽  
Quadratic Forms ◽  
Invariant Probability Measure ◽  
Markov Operator ◽  
Probability Measures ◽  
Infinite Dimensional ◽  
Stochastic Hamiltonian Systems ◽  
Integration By Parts Formula

By using the integration by parts formula of a Markov operator, the closability of quadratic forms associated to the corresponding invariant probability measure is proved. The general result is applied to the study of semilinear SPDEs, infinite-dimensional stochastic Hamiltonian systems, and semilinear SPDEs with delay.

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