Diffusion Monte Carlo: Exponential scaling of computational cost for large systems
نویسندگان
چکیده
منابع مشابه
Multilevel Monte Carlo for exponential Lévy models
We apply the multilevel Monte Carlo method for option pricing problems using exponential Lévy models with a uniform timestep discretisation. For lookback and barrier options, we derive estimates of the convergence rate of the error introduced by the discrete monitoring of the running supremum of a broad class of Lévy processes. We then use these to obtain upper bounds on the multilevel Monte Ca...
متن کاملExponential Integration for Hamiltonian Monte Carlo
We investigate numerical integration of ordinary differential equations (ODEs) for Hamiltonian Monte Carlo (HMC). High-quality integration is crucial for designing efficient and effective proposals for HMC. While the standard method is leapfrog (Störmer-Verlet) integration, we propose the use of an exponential integrator, which is robust to stiff ODEs with highly-oscillatory components. This os...
متن کاملMonte Carlo for Estimating Exponential Convolution
We study the numerical stability problem that may take place when calculating the cumulative distribution function of the Hypoexponential random variable. This computation is extensively used during the execution of Monte Carlo network reliability estimation algorithms. In spite of the fact that analytical formulas are available, they can be unstable in practice. This instability occurs frequen...
متن کاملSynchronous parallel kinetic Monte Carlo for continuum diffusion-reaction systems
A novel parallel kinetic Monte Carlo (kMC) algorithm formulated on the basis of perfect time synchronicity is presented. The algorithm is intended as a generalization of the standard w-fold kMC method, and is trivially implemented in parallel architectures. In its present form, the algorithm is not rigorous in the sense that boundary conflicts are ignored. We demonstrate, however, that, in thei...
متن کاملMonte Carlo Techniques for Data Assimilation in Large Systems
there is no need to derive a tangent linear operator or adjoint equations, and there are no integrations backward in time. EnKF is used extensively in a large community, including ocean and atmospheric sciences, oil reservoir simulations, and hydrological modeling. To a large extent EnKF overcomes two problems associated with the traditional KF. First, in KF an error covariance matrix for the m...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physical Review B
سال: 2010
ISSN: 1098-0121,1550-235X
DOI: 10.1103/physrevb.81.035119