The Onsager–Machlup functional for data assimilation
نویسنده
چکیده
Abstract. When taking the model error into account in data assimilation, one needs to evaluate the prior distribution represented by the Onsager–Machlup functional. Through numerical experiments, this study clarifies how the prior distribution should be incorporated into cost functions for discrete-time estimation problems. Consistent with previous theoretical studies, the divergence of the drift term is essential in weak-constraint 4D-Var (w4D-Var), but it is not necessary in Markov-chain Monte Carlo with the Euler scheme. Although the former property may cause difficulties when implementing w4D-Var in large 5
منابع مشابه
Transition paths in molecules at finite temperature
In the zero temperature limit, it is well known that in systems evolving via Brownian dynamics, the most likely transition path between reactant and product may be found as a minimizer of the Freidlin–Wentzell action functional. An analog for finite temperature transitions is given by the Onsager–Machlup functional. The purpose of this work is to investigate properties of Onsager– Machlup minim...
متن کاملExponential Estimates for Convex Norms and Some Applications
The role of correlation inequalities and martingale arguments in establishing conditional exponential bounds is reviewed. Applications to the computation of the Onsager Machlup functional for diiusions under non supremum norms follow.
متن کاملNonlinear smoothing for random fields
Stochastic nonlinear elliptic partial differential equations with white noise disturbances are studied in the countably additive measure set up. Introducing the Onsager-Machlup function to the system model, the smoothing problem for maximizing the modified likelihood functional is solved and the explicit form of nonlinear smoother is presented in the finitely additive observation noise set up. ...
متن کاملConditional exponential moments for iterated Wiener integrals
We provide sharp exponential moment bounds for (Stratonovich) iterated stochastic integrals under conditioning by certain small balls, including balls in certain HH older-like norms of exponent greater than 1=3. The proof uses a control of the variation of the L evy area, under conditioning. The results are applied to the computation of the Onsager-Machlup functional of diiusion processes with ...
متن کاملQuantum Macrostatistical Picture of Nonequilibrium Steady States
We apply our quantum macrostatistical treatment of irreversible processes [18] to prove that, in nonequilibrium steady states, (a) the hydrodynamical observables execute a generalised Onsager-Machlup [12] process and (b) the spatial correlations of these observables are generically of long range. The key assumptions behind these results are a nonequilibrium version of Onsager regression hypothe...
متن کامل