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作者：Beskos, Alexandros; Roberts, Gareth; Stuart, Andrew
作者单位：University of Warwick; University of Warwick
摘要：We investigate local MCMC algorithms, namely the random-walk Metropolis and the Langevin algorithms, and identify the optimal choice of the local step-size as a function of the dimension n of the state space, asymptotically as n -> infinity. We consider target distributions defined as a change of measure from a product law. Such structures arise, for instance, in inverse problems or Bayesian contexts when a product prior is combined with the likelihood. We state analytical results on the asymp...
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作者：Tanaka, Hideyuki; Kohatsu-Higa, Arturo
作者单位：Mitsubishi International Corporation (MIC); University of Osaka
摘要：Weak approximations have been developed to calculate the expectation value of functionals of stochastic differential equations, and various numerical discretization schemes (Euler, Milshtein) have been studied by many authors. We present a general framework based on semigroup expansions for the construction of higher-order discretization schemes and analyze its rate of convergence. We also apply it to approximate general Levy driven stochastic differential equations.
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作者：van Handel, Ramon
作者单位：Princeton University
摘要：A hidden Markov model is called observable if distinct initial laws give rise to distinct laws of the observation process. Observability implies stability of the nonlinear filter when the signal process is tight, but this need not be the case when the signal process is unstable. This paper introduces a stronger notion of uniform observability which guarantees stability of the nonlinear filter in the absence of stability assumptions on the signal. By developing certain uniform approximation pro...
