Related papers: Conditional probabilities in multiplicative noise …
In this work we detail the application of a fast convolution algorithm computing high dimensional integrals to the context of multiplicative noise stochastic processes. The algorithm provides a numerical solution to the problem of…
Non commutative quantum mechanics can be viewed as a quantum system represented in the space of Hilbert-Schmidt operators acting on non commutative configuration space. Taking this as departure point, we formulate a coherent state approach…
The effect of weak multiplicative colored noise on the dynamics of a Hamiltonian system is studied by means of asymptotic methods, in the vicinity of homoclinic or heteroclinic trajectories. A general expression for the probability of…
These lectures are intended as an introduction to the technique of path integrals and their applications in physics. The audience is mainly first-year graduate students, and it is assumed that the reader has a good foundation in quantum…
The Langevin formulation of a number of well-known stochastic processes involves multiplicative noise. In this work we present a systematic mapping of a process with multiplicative noise to a related process with additive noise, which may…
In stochastic resonance, a periodically forced Brownian particle in a double-well potential jumps between minima at rare increments, the prediction of which poses a major theoretical challenge. Here, we use a path-integral method to find a…
There are many advantages to use probability method for nonlinear system identification, such as the noises and outliers in the data set do not affect the probability models significantly; the input features can be extracted in probability…
This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…
We present a consistent method to calculate the probability distribution of soliton parameters in systems with additive noise. Even though a weak noise is considered, we are interested in probabilities of large fluctuations (generally…
The manner in which probability amplitudes of paths sum up to form wave functions of a harmonic oscillator, as well as other, simple 1-dimensional problems, is described. Using known, closed-form, path-based propagators for each problem, an…
We develop a convergent variational perturbation theory for conditional probability densities of Markov processes. The power of the theory is illustrated by applying it to the diffusion of a particle in an anharmonic potential.
This article deals with the approximation of a stochastic partial differential equation (SPDE) via amplitude equations. We consider an SPDE with a cubic nonlinearity perturbed by a general multiplicative noise that preserves the constant…
In the probability representation of the standard quantum mechanics, the explicit expression (and its quasiclassical van-Fleck approximation) for the ``classical'' propagator (transition probability distribution), which completely describes…
We give a pedagogical review of the application of field theoretic and path integral methods to calculate moments of the probability density function of stochastic differential equations perturbatively.
We consider a simple model of a bistable system under the influence of multiplicative noise. We provide a path integral representation of the overdamped Langevin dynamics and compute conditional probabilities and escape rates in the weak…
For a model nonlinear dynamical system, we show how one may obtain its bifurcation behavior by introducing noise into the dynamics and then studying the resulting Langevin dynamics in the weak-noise limit. A suitable quantity to capture the…
Multiplicative noise models are often used instead of additive noise models in cases in which the noise variance depends on the state. Furthermore, when Poisson distributions with relatively small counts are approximated with normal…
Stochastic processes with multiplicative noise have been studied independently in several different contexts over the past decades. We focus on the regime, found for a generic set of control parameters, in which stochastic processes with…
We perturb with an additive Gaussian white noise the Hamiltonian system associated to a cubic anharmonic oscillator. The stochastic system is assumed to start from initial conditions that guarantee the existence of a periodic solution for…
As inductive inference and machine learning methods in computer science see continued success, researchers are aiming to describe ever more complex probabilistic models and inference algorithms. It is natural to ask whether there is a…