Journal ArticleDOI
Monte carlo evaluation of functionals of solutions of stochastic differential equations. variance reduction and numerical examples
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Variance-reducing estimators for functionals of the solution of the general Ito stochastic differential equation are derived in this article, which allow to apply variance reduction techniques known from the Monte Carlo theory.Abstract:
Variance–reducing estimators are derived for functionals of the solution of the general Ito stochastic differential equation. These estimators allow to apply variance reduction techniques known from the Monte Carlo theory. In particular, variance–reducing Euler estimators are constructed as well as variance–reducing unbiased estimators. Numerical examples are given. They show that the variance reduction techniques cause an enormous gain in efficiency, reducing the statistical error up to 50 times. They also demonstrate the effect of the unbiased estimators, which allow to evaluate the functionals without reducing the time step.read more
Citations
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Journal ArticleDOI
Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes (with discussion)
TL;DR: Monte Carlo methods are proposed, which build on recent advances on the exact simulation of diffusions, for performing maximum likelihood and Bayesian estimation for discretely observed diffusions.
Journal ArticleDOI
An introduction to numerical methods for stochastic differential equations
TL;DR: In this article, the authors give an overview and summary of numerical methods for the solution of stochastic differential equations, covering discrete time strong and weak approximation methods that are suitable for different applications.
Journal ArticleDOI
Speeding Up MCMC by Efficient Data Subsampling
TL;DR: Subsampling Markov chain Monte Carlo is substantially more efficient than standard MCMC in terms of sampling efficiency for a given computational budget, and that it outperforms other subsampling methods for MCMC proposed in the literature.
Journal ArticleDOI
The Euler scheme with irregular coefficients
TL;DR: Weak convergence of the Euler scheme for stochastic differential equations is established when coefficients are discontinuous on a set of Lebesgue measure zero as mentioned in this paper, and the rate of convergence is presented for coefficients are Holder continuous.
Journal ArticleDOI
Dynamic reaction paths and rates through importance-sampled stochastic dynamics
TL;DR: In this article, a method based on Wagner's stochastic formulation of importance sampling is extended to the calculation of reaction rates and to a simple quantitative description of finite-temperature, average dynamic paths.
References
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Book
Stochastic processes in physics and chemistry
TL;DR: In this article, the authors introduce the Fokker-planck equation, the Langevin approach, and the diffusion type of the master equation, as well as the statistics of jump events.
Stochastic Processes in Physics and Chemistry
Abstract: Preface to the first edition. Preface to the second edition. Abbreviated references. I. Stochastic variables. II. Random events. III. Stochastic processes. IV. Markov processes. V. The master equation. VI. One-step processes. VII. Chemical reactions. VIII. The Fokker-Planck equation. IX. The Langevin approach. X. The expansion of the master equation. XI. The diffusion type. XII. First-passage problems. XIII. Unstable systems. XIV. Fluctuations in continuous systems. XV. The statistics of jump events. XVI. Stochastic differential equations. XVII. Stochastic behavior of quantum systems.
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Stochastic differential equations and diffusion processes
TL;DR: In this article, Stochastic Differential Equations and Diffusion Processes are used to model the diffusion process in stochastic differential equations. But they do not consider the nonlinearity of diffusion processes.
Book ChapterDOI
Stochastic Differential Equations
TL;DR: In this paper, the authors return to the possible solutions X t (ω) of the stochastic differential equation where W t is 1-dimensional "white noise" and where X t satisfies the integral equation in differential form.