Related papers: Instanton filtering for the stochastic Burgers equ…
A highly efficient formulation of moment equations for stochastic reaction networks is introduced. It is based on a set of binomial moments that capture the combinatorics of the reaction processes. The resulting set of equations can be…
This work deals with the one-dimensional Stefan problem with a general time-dependent boundary condition at the fixed boundary. Stochastic solutions are obtained using discrete random walks, and the results are compared with analytic…
Instantons play a crucial role in understanding non-perturbative dynamics in quantum field theories, including those with spontaneously broken gauge symmetries. In the broken phase, finite-size instanton-like configurations are no longer…
The solution of a (stochastic) differential equation (SDE) can be locally approximated by a stochastic expansion, a linear combination of iterated integrals. Quantities of interest, like moments, can then be approximated with the expansion.…
We present an approach for testing for the existence of continuous generators of discrete stochastic transition matrices. Typically, the known approaches to ascertain the existence of continuous Markov processes are based in the assumption…
Piecewise-deterministic Markov processes combine continuous in time dynamics with jump events, the rates of which generally depend on the continuous variables and thus are not constants. This leads to a problem in a Monte-Carlo simulation…
Stochastic reaction network models arise in intracellular chemical reactions, epidemiological models and other population process models, and are a class of continuous time Markov chains which have the nonnegative integer lattice as state…
Path integral implementation of the quantum instanton approximation currently belongs among the most accurate methods for computing quantum rate constants and kinetic isotope effects, but its use has been limited due to the rather high…
We study the stochastic Burgers equation driven by an additive Hermite sheet of order $q \ge 1$. The equation is formulated in the mild sense using the heat semigroup, and existence and uniqueness of solutions are established via a…
How systems transit between different stable states under external perturbation is an important practical issue. We discuss here how a recently-developed energy optimization method for identifying the minimal disturbance necessary to reach…
We study the instanton effects of the ABJM partition function using the Fermi gas formalism. We compute the exact values of the partition function at the Chern-Simons levels k=1,2,3,4,6 up to N=44,20,18,16,14 respectively, and extract…
A continuous-time Markov chain rate change formula for simulation, model selection, filtering and theory is proven. It is used to develop Markov chain importance sampling, rejection sampling, branching particle filtering algorithms and…
Instanton theory relates the rate constant for tunneling through a barrier to the periodic classical trajectory on the upturned potential energy surface whose period is $\tau=\hbar/(k_{\rm B}T)$. Unfortunately, the standard theory is only…
Exactly solvable variable parametric Burgers type equations in one-dimension are introduced, and two different approaches for solving the corresponding initial value problems are given. The first one is using the relationship between the…
We study the class of one-dimensional equations driven by a stochastic measure $\mu$. For $\mu$ we assume only $\sigma$-additivity in probability. This class of equations include the Burgers equation and the heat equation. The existence and…
We develop a Gaussian process regression enhanced line integral string method to accelerate ring polymer instanton calculations of tunneling rates and tunneling splittings in molecular proton transfer reactions. By exploiting uncertainty…
Applications of stochastic models often involve the evaluation of steady-state performance, which requires solving a set of balance equations. In most cases of interest, the number of equations is infinite or even uncountable. As a result,…
In this paper we propose an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial differential equations (SPDEs) with non-globally monotone…
In five spacetime dimensions, instantons are finite energy, solitonic particles. We describe the dynamics of these objects in the presence of a Chern-Simons interaction. For U(N) instantons, we show that the 5d Chern-Simons term induces a…
Using the instanton representation method, we re-construct graviton solutions about DeSitter spacetime. We have used this example as a testing arena to expose the internal structure of the method and to establish that it works for known…