In the present work advanced Monte Carlo methods for discrete-time stochastic processes are developed and investigated. A particular focus is on sequential Monte Carlo methods (particle filters and particle smoothers) which allow the estimation of nonlinear, non-Gaussian state-space models. The key technique which underlies the proposed algorithms is importance sampling. Computationally efficient nonparametric variants of importance sampling which are generally applicable are developed. Asymptotic properties of these methods are analyzed theoretically and it is shown empirically that they improve over existing methods for relevant applications. Particularly, it is shown that they can be applied for financial derivative pricing which constitutes a high-dimensional integration problem and that they can be used to improve sequential Monte Carlo methods. Original models in general state-space form for two important applications are proposed and new sequential Monte Carlo algorithms for their estimation are developed. The first application concerns the on-line estimation of the spot cross-volatility for ultra high-frequency financial data. This is a challenging problem because of the presence of microstructure noise and nonsynchronous trading. For the first time state-space models with non-synchronously evolving states and observations are discussed and a particle filter which can cope with these models is designed. In addition, a new sequential variant of the EM algorithm for parameter estimation is proposed. The second application is a non-linear model for time series with an oscillatory pattern and a phase process in the background. This model can be applied, for instance, to noisy quasiperiodic oscillators occurring in physics and other fields. The estimation of the model is based on an advanced particle smoother and a new nonparametric EM algorithm. The dissertation is accompanied by object-oriented C++ implementations of all proposed algorithms which were developed with a focus on reusability and extendability
