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We briefly review the principles, mathematical bases, numerical shortcuts and applications of fast random walk (FRW) algorithms. This Monte Carlo technique allows one to simulate individual trajectories of diffusing particles in order to…
We present the particle method for simulating the solution to the path-dependent McKean-Vlasov equation, in which both the drift and the diffusion coefficients depend on the whole trajectory of the process up to the current time t, as well…
In this paper we introduce an approximate method to solve the quantum cavity equations for transverse field Ising models. The method relies on a projective approximation of the exact cavity distributions of imaginary time trajectories…
Stable computational algorithms for the approximate solution of the Cauchy problem for nonstationary problems are based on implicit time approximations. Computational costs for boundary value problems for systems of coupled multidimensional…
This paper is devoted to the homogenization of weakly coupled cooperative parabolic systems in strong convection regime with purely periodic coefficients. Our approach is to factor out oscillations from the solution via principal…
We set-up and solve the Cauchy problem for Schr\"odinger-type differential operators with generalized functions as coefficients, in particular, allowing for distributional coefficients in the principal part. Equations involving such kind of…
Towards identifying the number of minimal surfaces sharing the same boundary from the geometry of the boundary, we propose a numerical scheme with high speed and high accuracy. Our numerical scheme is based on the method of fundamental…
A new Monte-Carlo method for solving linear parabolic partial differential equations is presented. Since, in this new scheme, the particles are followed backward in time, it provides great flexibility in choosing critical points in…
We introduce Monte Carlo methods to compute the solution of elliptic equations with pure Neumann boundary conditions. We first prove that the solution obtained by the stochastic representation has a zero mean value with respect to the…
We consider the Cauchy problem for a class of nonlinear degenerate parabolic equa- tion with forcing. By using the vanishing viscosity method we obtain generalized solutions. We prove some regularity results about this generalized…
In this paper is described a general 2-nd order accurate (weak sense) procedure for stablizing Monte-Carlo simulations of Ito stochastic differential equations. The splitting procedure includes explicit Runge-Kutta methods, semi-implicit…
Stochastic quantization in physics has been considered to provide a path integral representation of a probability distribution for Ito processes. It has been indicated that the stochastic quantization can involve a potential term, if the…
The use of sequential Monte Carlo within simulation for path-dependent option pricing is proposed and evaluated. Recently, it was shown that explicit solutions and importance sampling are valuable for efficient simulation of spot price and…
This work focuses on the derivation and the analysis of a novel, strongly-coupled partitioned method for fluid-structure interaction problems. The flow is assumed to be viscous and incompressible, and the structure is modeled using linear…
We describe an exact and highly efficient numerical algorithm for solving a special but important class of convection-diffusion equations. These equations occur in many problems in physics, chemistry, or biology, and they are usually hard…
We develop a new numerical scheme which allows precise solution of coherent tunneling problems, i.e., problems with exponentially small transition amplitudes between quasidegenerate states. We explain how this method works for the…
In this paper, three efficient ensemble algorithms are proposed for fast-solving the random fluid-fluid interaction model. Such a model can be simplified as coupling two heat equations with random diffusion coefficients and a friction…
This topical review describes the methodology of continuum variational and diffusion quantum Monte Carlo calculations. These stochastic methods are based on many-body wave functions and are capable of achieving very high accuracy. The…
With a view to statistical inference for discretely observed diffusion models, we propose simple methods of simulating diffusion bridges, approximately and exactly. Diffusion bridge simulation plays a fundamental role in likelihood and…
We explore two complementary modifications of the hybridization-expansion continuous-time Monte Carlo method, aiming at large multi-orbital quantum impurity problems. One idea is to compute the imaginary-time propagation using a matrix…