@phdthesis{Neureither2019, author = {Neureither, Lara}, title = {Irreversible multi-scale diffusions: time scales and model reduction}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-50467}, school = {BTU Cottbus - Senftenberg}, year = {2019}, abstract = {In this work, we consider non-reversible multi-scale stochastic processes, described by stochastic differential equations, for which we review theory on the convergence behaviour to equilibrium and mean first exit times. Relations between these time scales for non-reversible processes are established, and, by resorting to a control theoretic formulation of the large deviations action functional, even the consideration of hypo-elliptic processes is permitted. The convergence behaviour of the processes is studied in a lot of detail, in particular with respect to initial conditions and temperature. Moreover, the behaviour of the conditional and marginal distributions during the relaxation phase is monitored and discussed as we encounter unexpected behaviour. In the end, this results in the proposal of a data-based partitioning into slow and fast degrees of freedom. In addition, recently proposed techniques promising accelerated convergence to equilibrium are examined and a connection to appropriate model reduction approaches is made. For specific examples this leads to either an interesting alternative formulation of the acceleration procedure or structural insight into the acceleration mechanism. For the model order reduction technique of effective dynamics, which uses conditional expectations, error bounds for non-reversible slow-fast stochastic processes are obtained. A comparison with the reduction method of averaging is undertaken, which, for non-reversible processes, possibly yields different reduced equations. For Ornstein-Uhlenbeck processes sufficient conditions are derived for the two methods (effective dynamics and averaging) to agree in the infinite time scale separation regime. Additionally, we provide oblique projections which allow for the sampling of conditional distributions of non-reversible Ornstein-Uhlenbeck processes.}, subject = {Model reduction; Non-reversible diffusions; Relative entropy; Convergence to steady state; Conditional expectation; Modellreduktion; Nicht-reversible Diffusionen; Relative Entropie; Konvergenz gegen den Gleichgewichtszustand; Bedingte Erwartung; Ordnungsreduktion; Molekulardynamik; Diffusionsprozess; Bedingter Erwartungswert}, language = {en} }