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Fokker-Planck equations are extensively employed in various scientific fields as they characterise the behaviour of stochastic systems at the level of probability density functions. Although broadly used, they allow for analytical treatment…
In recent years, there has been remarkable progress in theoretical justification of the complex Langevin method, which is a promising method for evading the sign problem in the path integral with a complex weight. There still remains,…
We model thermostatic devices using a stochastic hybrid description, and introduce an external actuation mechanism that creates random switch events in the discrete dynamics. We then conjecture the form of the Fokker-Planck equation and…
We present a method for constructing numerical schemes with up to 3rd strong convergence order for solution of a class of stochastic differential equations, including equations of the Langevin type. The construction proceeds in two stages.…
The rigorous linking of exact stochastic models to mean-field approximations is studied. Starting from the differential equation point of view the stochastic model is identified by its Kolmogorov equations, which is a system of linear ODEs…
Matrix determinants play an important role in data analysis, in particular when Gaussian processes are involved. Due to currently exploding data volumes, linear operations - matrices - acting on the data are often not accessible directly…
Reaction diffusion systems describe the behaviour of dynamic, interacting, particulate systems. Quantum stochastic processes generalise Brownian motion and Poisson processes, having operator valued It\^{o} calculus machinery. Here it is…
The paper studies a class of quantum stochastic differential equations, modeling an interaction of a system with its environment in the quantum noise approximation. The space representing quantum noise is the symmetric Fock space over…
Stochastic exclusion processes play an integral role in the physics of non-equilibrium statistical mechanics. These models are Markovian processes, described by a classical master equation. In this paper a quantum mechanical version of a…
After collecting data from observations or experiments, the next step is to build an appropriate mathematical or stochastic model to describe the data so that further studies can be done with the help of the models. In this article, the…
Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…
Cellular reactions have multi-scale nature in the sense that the abundance of molecular species and the magnitude of reaction rates can vary in a wide range. This diversity leads to hybrid models that combine deterministic and stochastic…
The success of quantum physics in description of various physical interaction phenomena relies primarily on the accuracy of analytical methods used. In quantum mechanics, many of such interactions such as those found in quantum…
Numerical studies of the May-Leonard model for cyclically competing species exhibit spontaneous spatial structures in the form of spirals. It is desirable to obtain a simple coarse-grained evolution equation describing spatio-temporal…
A stochastic field theory approach is applied to a coarse-grained polymer model that will enable studies of polymer behavior under non-equilibrium conditions. This article is focused on the validation of the new model in comparison to…
We examine the three-step master equation from the standpoint of the general solution of the associated discrete Riccati equation. We report by this means stationary master solutions depending on a free constant parameter, denoted by D,…
Simulations of stochastic processes play an important role in the quantitative sciences, enabling the characterisation of complex systems. Recent work has established a quantum advantage in stochastic simulation, leading to quantum devices…
We propose a novel method to solve a chemical diffusion master equation of birth and death type. This is an infinite system of Fokker-Planck equations where the different components are coupled by reaction dynamics similar in form to a…
We develop a variational scheme in a field theoretic approach to a stochastic process. While various stochastic processes can be expressed using master equations, in general it is difficult to solve the master equations exactly, and it is…
The theory of stochastic processes impacts both physical and social sciences. At the molecular scale, stochastic dynamics is ubiquitous because of thermal fluctuations. The Fokker-Plank-Smoluchowski equation models the time evolution of the…