In the design of efficient simulation algorithms, one is often beset with a poor choice of proposal distributions. Although the performance of a given simulation kernel can clarify a posteriori how adequate this kernel is for the problem at hand, a p
ermanent on-line modification of kernels causes concerns about the validity of the resulting algorithm. While the issue is most often intractable for MCMC algorithms, the equivalent version for importance sampling algorithms can be validated quite precisely. We derive sufficient convergence conditions for adaptive mixtures of population Monte Carlo algorithms and show that Rao--Blackwelliz
Taking into account some likeness of moderate deviations (MD) and central limit theorems (CLT), we develop an approach, which made a good showing in CLT, for MD analysis of a family $$ S^kappa_t=frac{1}{t^kappa}int_0^tH(X_s)ds, ttoinfty $$ for an er
godic diffusion process $X_t$ under $0.5<kappa<1$ and appropriate $H$. We mean a decomposition with ``corrector: $$ frac{1}{t^kappa}int_0^tH(X_s)ds={rm corrector}+frac{1}{t^kappa}underbrace{M_t}_{rm martingale}. $$ and show that, as in the CLT analysis, the corrector is negligible but in the MD scale, and the main contribution in the MD brings the family ``$ frac{1}{t^kappa}M_t, ttoinfty. $ Starting from Bayer and Freidlin, cite{BF}, and finishing by Wus papers cite{Wu1}-cite{WuH}, in the MD study Laplaces transform dominates. In the paper, we replace the Laplace technique by one, admitting to give the conditions, providing the MD, in terms of ``drift-diffusion parameters and $H$. However, a verification of these conditions heavily depends on a specificity of a diffusion model. That is why the paper is named ``Examples ....
We first give a characterization of the L^1-transportation cost-information inequality on a metric space and next find some appropriate sufficient condition to transportation cost-information inequalities for dependent sequences. Applications to random dynamical systems and diffusions are studied.
Consider the state space model (X_t,Y_t), where (X_t) is a Markov chain, and (Y_t) are the observations. In order to solve the so-called filtering problem, one has to compute L(X_t|Y_1,...,Y_t), the law of X_t given the observations (Y_1,...,Y_t). Th
e particle filtering method gives an approximation of the law L(X_t|Y_1,...,Y_t) by an empirical measure frac{1}{n}sum_1^ndelta_{x_{i,t}}. In this paper we establish the moderate deviation principle for the empirical mean frac{1}{n}sum_1^npsi(x_{i,t}) (centered and properly rescaled) when the number of particles grows to infinity, enhancing the central limit theorem. Several extensions and examples are also studied.
We establish large deviation principle (LDP) for the family of vector-valued random processes $(X^epsilon,Y^epsilon),epsilonto 0$ defined as $$ X^epsilon_t=frac{1}{epsilon^kappa}int_0^t H(xi^epsilon_s,Y^epsilon_s)ds, dY^epsilon_t=F(xi^epsilon_t,Y^eps
ilon_t)dt+ Depsilon^{1/2-kappa}G(xi^epsilon_t,Y^epsilon_t)dW_t,$$ where $W_t$ is Wiener process and $xi^epsilon_t$ is fast ergodic diffusion. We show that, under $kappa<{1/2}$ or less and Veretennikov-Khasminskii type condition for fast diffusion, the LDP holds with rate function of Freidlin-Wentzells type.
