相关论文: Redundant basis interpretation of Doi-Peliti metho…
Duality relations between continuous-state and discrete-state stochastic processes with continuous-time have already been studied and used in various research fields. We propose extended duality relations, which enable us to derive…
Fluctuation theorems may be partitioned into those that apply the probability measure under the original stochastic process to reversed paths, and those that construct a new, adjoint measure by similarity transform, which locally reverses…
A form of time series path integral expansion is provided that enables both analytic and numerical temporal effect calculations for a range of stochastic processes. Birth-death processes with linear rates are analysed via coherent state…
In the context of Markov processes, we show a new scheme to derive dual processes and a duality function based on a boson representation. This scheme is applicable to a case in which a generator is expressed by boson creation and…
An extension of the Doi-Peliti formalism for stochastic chemical kinetics is proposed. Using the extension, path-integral expressions consistent with previous studies are obtained. In addition, the extended formalism is naturally connected…
We present an approach to the dynamics of interacting particle systems, which allows to derive path integral formulas from purely stochastic considerations. We show that the resulting field theory is a dual version of the standard theory of…
The long term aim is to use modern dynamical systems theory to derive discretisations of noisy, dissipative partial differential equations. As a first step we here consider a small domain and apply stochastic centre manifold techniques to…
By combining the two-particle-irreducible (2PI) effective action common in non-equilibrium quantum field theory with the classical Martin-Siggia-Rose formalism, self-consistent equations of motion for the first and second cumulants of…
We extend our discussion of effective actions for stochastic partial differential equations to systems that give rise to a Martin-Siggia-Rose (MSR) type of action. This type of action naturally arises when one uses the many-body formalism…
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…
A new derivation method of duality relations in stochastic processes is proposed. The current focus is on the duality between stochastic differential equations and birth-death processes. Although previous derivation methods have been based…
Gradient-based techniques are becoming increasingly critical in quantitative fields, notably in statistics and computer science. The utility of these techniques, however, ultimately depends on how efficiently we can evaluate the derivatives…
This note shows how classical tools from linear control theory can be leveraged to provide a global analysis of nonlinear reaction-diffusion models. The approach is differential in nature. It proceeds from classical tools of contraction…
Stochastic differential equations (SDE) are widely used in modeling stochastic dynamics in literature. However, SDE alone is not enough to determine a unique process. A specified interpretation for stochastic integration is needed.…
In this article we develop a new methodology to prove weak approximation results for general stochastic differential equations. Instead of using a partial differential equation approach as is usually done for diffusions, the approach…
This paper provides a probabilistic approach to solve linear equations involving Caputo and Riemann-Liouville type derivatives. Using the probabilistic interpretation of these operators as the generators of interrupted Feller processes, we…
Variational integrators are derived for structure-preserving simulation of stochastic Hamiltonian systems with a certain type of multiplicative noise arising in geometric mechanics. The derivation is based on a stochastic discrete…
This paper presents an innovative approach, the Adaptive Orthogonal Basis Method, tailored for computing multiple solutions to differential equations characterized by polynomial nonlinearities. Departing from conventional practices of…
We present a method that captures the fluctuations beyond mean field in chemical reactions in the regime of small copy numbers and hence large fluctuations, using self-consistently determined memory: by integrating information from the past…
We consider a class of parameter-dependent optimal control problems of elliptic PDEs with constraints of general type on the control variable. Applying the concept of variational discretization, [4], together with techniques from the…