Related papers: Stochastic path power and the Laplace transform
The time evolution of many physical, chemical, and biological systems can be modelled by stochastic transitions between the minima of the potential energy surface describing the system of interest. We show that in cases where there are two…
We introduce a path sampling method for obtaining statistical properties of an arbitrary stochastic dynamics. The method works by decomposing a trajectory in time, estimating the probability of satisfying a progress constraint, modifying…
We recently proposed a method for estimation of states and parameters in stochastic differential equations, which included intermediate time points between observations and used the Laplace approximation to integrate out these intermediate…
The evaluation of the path-integral representation for stochastic processes in the weak-noise limit shows that these systems are governed by a set of equations which are those of a classical dynamics. We show that, even when the noise is…
Stochastic dynamical systems allow modelling of transitions induced by disturbances, in particular from an attracting equilibrium and crossing the stable manifold of a saddle. In the small-noise limit, the probability of such transitions is…
Stochastic systems often exhibit multiple viable metastable states that are long-lived. Over very long timescales, fluctuations may push the system to transition between them, drastically changing its macroscopic configuration. In realistic…
The path probability of stochastic motion of non dissipative or quasi-Hamiltonian systems is investigated by numerical experiment. The simulation model generates ideal one-dimensional motion of particles subject only to conservative forces…
A two-type continuous-state branching process in varying environments is constructed as the pathwise unique solution of a system of stochastic equations driven by time-space noises, where the pathwise uniqueness is derived from a comparison…
We present a path integral formalism to compute potentials for nonequilibrium steady states, reached by a multiplicative stochastic dynamics. We develop a weak-noise expansion, which allows the explicit evaluation of the potential in…
We address the role of noise and the issue of efficient computation in stochastic optimal control problems. We consider a class of non-linear control problems that can be formulated as a path integral and where the noise plays the role of…
This paper considers linear-quadratic control of a non-linear dynamical system subject to arbitrary cost. I show that for this class of stochastic control problems the non-linear Hamilton-Jacobi-Bellman equation can be transformed into 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…
An estimation method is proposed for a wide variety of discrete time stochastic processes that have an intractable likelihood function but are otherwise conveniently specified by an integral transform such as the characteristic function,…
An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…
This work is devoted to the investigation of the most probable transition time between metastable states for stochastic dynamical systems. Such a system is modeled by a stochastic differential equation with non-vanishing Brownian noise, and…
Global dynamics in nonlinear stochastic systems is often difficult to analyze rigorously. Yet, many excellent numerical methods exist to approximate these systems. In this work, we propose a method to bridge the gap between computation and…
By using path integrals, the stochastic process associated to the time evolution of the quantum probability density is formally rewritten in terms of a stochastic differential equation, given by Newton's equation of motion with an…
Stochastically switching force terms appear frequently in models of biological systems under the action of active agents such as proteins. The interaction of switching force and Brownian motion can create an "effective thermal equilibrium"…
We derive the differential equation describing the time evolution of the work probability distribution function of a stochastic system which is driven out of equilibrium by the manipulation of a parameter. We consider both systems described…
Biomolecular folding, at least in simple systems, can be described as a two state transition in a free energy landscape with two deep wells separated by a high barrier. Transition paths are the short part of the trajectories that cross the…