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We extend Monte Carlo samplers based on piecewise deterministic Markov processes (PDMP samplers) by formally defining different boundary conditions such as sticky floors, soft and hard walls and teleportation portals. This allows PDMP…

Computation · Statistics 2023-03-15 Joris Bierkens , Sebastiano Grazzi , Gareth Roberts , Moritz Schauer

In the first part of this paper we study approximations of trajectories of Piecewise Deter-ministic Processes (PDP) when the flow is not explicit by the thinning method. We also establish a strong error estimate for PDPs as well as a weak…

Probability · Mathematics 2022-02-10 Vincent Lemaire , Michèle Thieullen , Nicolas Thomas

In this paper we develop a general framework for constructing and analysing coupled Markov chain Monte Carlo samplers, allowing for both (possibly degenerate) diffusion and piecewise deterministic Markov processes. For many performance…

Probability · Mathematics 2018-06-29 N. Nuesken , G. A. Pavliotis

Robust inference for stochastic dynamical systems is often hampered by sparse sampling and the absence of closed-form likelihoods. We introduce a Monte Carlo path-inference framework that leverages full-path statistics and bridge processes…

Statistical Mechanics · Physics 2025-10-07 Javier Aguilar , Miguel A. Muñoz , Sandro Azaele

A deterministic-stochastic coupling scheme is developed for simulating rarefied gas flows, where the key process is the alternative solving of the macroscopic synthetic equations [Su et al., J. Comput. Phys., 407 (2020) 109245] and the…

Computational Physics · Physics 2024-06-26 Liyan Luo , Qi Li , Fei Fei , Lei Wu

In this work we propose a hierarchy of Monte Carlo methods for sampling equilibrium properties of stochastic lattice systems with competing short and long range interactions. Each Monte Carlo step is composed by two or more sub - steps…

Numerical Analysis · Mathematics 2015-05-30 Evangelia Kalligiannaki , Markos A. Katsoulakis , Petr Plechac , Dionisios G Vlachos

An efficient Path Integral Monte Carlo procedure is proposed to simulate the behavior of quantum many-body dissipative systems described within the framework of the influence functional. Thermodynamic observables are obtained by Monte Carlo…

Statistical Mechanics · Physics 2009-11-07 Luca Capriotti , Alessandro Cuccoli , Andrea Fubini , Valerio Tognetti , Ruggero Vaia

This chapter is devoted to the computation of equilibrium (thermodynamic) properties of quantum systems. In particular, we will be interested in the situation where the interaction between particles is so strong that it cannot be treated as…

Mesoscale and Nanoscale Physics · Physics 2016-02-03 Alexei Filinov , Jens Böning , Michael Bonitz

Large deviations for additive path functionals of stochastic processes have attracted significant research interest, in particular in the context of stochastic particle systems and statistical physics. Efficient numerical `cloning'…

Probability · Mathematics 2021-07-21 Letizia Angeli , Stefan Grosskinsky , Adam M. Johansen

While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC…

Numerical Analysis · Mathematics 2017-12-20 Ralf Kornhuber , Evgenia Youett

Stochastic computational models in the form of pure jump processes occur frequently in the description of chemical reactive processes, of ion channel dynamics, and of the spread of infections in populations. For spatially extended models,…

Numerical Analysis · Mathematics 2018-02-23 Augustin Chevallier , Stefan Engblom

This simple note lays out a few observations which are well known in many ways but may not have been said in quite this way before. The basic idea is that when comparing two different Markov chains it is useful to couple them is such a way…

Probability · Mathematics 2017-11-16 James E. Johndrow , Jonathan C. Mattingly

Path integrals with complex actions are encountered for many physical systems ranging from spin- or mass-imbalanced atomic gases and graphene to quantum chromo-dynamics at finite density to the non-equilibrium evolution of quantum systems.…

High Energy Physics - Lattice · Physics 2022-09-01 Lukas Kades , Martin Gärttner , Thomas Gasenzer , Jan M. Pawlowski

A goal of systems biology is to understand the dynamics of intracellular systems. Stochastic chemical kinetic models are often utilized to accurately capture the stochastic nature of these systems due to low numbers of molecules. Collecting…

Computation · Statistics 2015-03-17 Jarad Niemi , Matthew Wheeler

Reaction networks are often used to model interacting species in fields such as biochemistry and ecology. When the counts of the species are sufficiently large, the dynamics of their concentrations are typically modeled via a system of…

Numerical Analysis · Mathematics 2022-01-05 David F. Anderson , Kurt W. Ehlert

We show how to extend a recently proposed multi-level Monte Carlo approach to the continuous time Markov chain setting, thereby greatly lowering the computational complexity needed to compute expected values of functions of the state of the…

Probability · Mathematics 2011-11-23 David F. Anderson , Desmond J. Higham

Piecewise deterministic Markov processes (PDMPs) are a class of stochastic processes with applications in several fields of applied mathematics spanning from mathematical modeling of physical phenomena to computational methods. A PDMP is…

Probability · Mathematics 2022-09-30 Andrea Bertazzi , Joris Bierkens , Paul Dobson

Traditional gradient-based sampling methods, like standard Hamiltonian Monte Carlo, require that the desired target distribution is continuous and differentiable. This limits the types of models one can define, although the presented models…

Computation · Statistics 2025-04-28 Jimmy Huy Tran , Tore Selland Kleppe

Recently, a class of stochastic processes known as piecewise deterministic Markov processes has been used to define continuous-time Markov chain Monte Carlo algorithms with a number of attractive properties, including compatibility with…

Computation · Statistics 2019-06-03 Alexander Terenin , Daniel Thorngren

Biochemical reaction networks frequently consist of species evolving on multiple timescales. Stochastic simulations of such networks are often computationally challenging and therefore various methods have been developed to obtain sensible…

Molecular Networks · Quantitative Biology 2017-04-20 Jae Kyoung Kim , Grzegorz A. Rempala , Hye-Won Kang