High order splitting schemes with complex timesteps are applied to Kolmogorov backward equations stemming from stochastic differential equations in Stratonovich form. In the setting of weighted spaces, the necessary analyticity of the split semigroups can be easily proved. A numerical example from interest rate theory, the CIR2 model, is considered. The numerical results are robust for drift-do...

The problem of strongly correlated electrons in one dimension attracted the attention of condensed matter physicists since early 50’s. After the seminal paper of Tomonaga [8] who suggested the first soluble model in 1950, there were essential achievements reflected in papers by Luttinger [6] (1963) and Mattis and Lieb [7] (1963). Considerable contribution to understanding of the generic propert...

in this paper, a class of semi-implicit two-stage stochastic runge-kutta methods (srks) of strong global order one, with minimum principal error constants are given. these methods are applied to solve itô stochastic differential equations (sdes) with a wiener process. the efficiency of this method with respect to explicit two-stage itô runge-kutta methods (irks), it method, milstien method, sem...

Lattice spin models in statistical physics are used to understand magnetism. Their Hamiltonians a discrete form of version Dirichlet energy, signifying relationship the Harmonic map heat flow equation. The Gibbs distribution, defined with this Hamiltonian, is Metropolis-Hastings (M-H) algorithm generate dynamics tending towards an equilibrium state. In limiting situation when inverse temperatur...

The quantum Monte Carlo method on asymptotic Lefschetz thimbles is a numerical algorithm devised specifically for alleviation of the sign problem appearing in simulations many-body systems. In this method, alleviated by shifting integration domain auxiliary fields, appearing, example, conventional determinant from real space to an appropriate manifold complex space. Here, we extend spin models ...