Related papers: Continuity equation for probability as a requireme…
The method of choice for integrating the time-dependent Fokker-Planck equation in high-dimension is to generate samples from the solution via integration of the associated stochastic differential equation. Here, we study an alternative…
The Fokker-Planck equation can be reformulated as a continuity equation, which naturally suggests using the associated velocity field in particle flow methods. While the resulting probability flow ODE offers appealing properties - such as…
We consider the solvability of the Fokker-Planck equation with both time-dependent drift and diffusion coefficients by means of the similarity method. By the introduction of the similarity variable, the Fokker-Planck equation is reduced to…
One of the cornerstones in non--equilibrium statistical mechanics (NESM) is Liouville's theorem, a differential equation for the phase space probability $\rho(q,p; t)$. This is usually derived considering the flow in or out of a given…
By investigating path-distribution dependent stochastic differential equations, the following type of nonlinear Fokker--Planck equations for probability measures $(\mu_t)_{t \geq 0}$ on the path space $\mathcal C:=C([-r_0,0];\mathbb R^d),$…
In this work, we consider the solvability of the Fokker-Planck equation with both time-dependent drift and diffusion coefficients by means of the similarity method. By the introduction of the similarity variable, the Fokker-Planck equation…
Maximization of the path information entropy is a clear prescription for constructing models in non-equilibrium statistical mechanics. Here it is shown that, following this prescription under the assumption of arbitrary instantaneous…
The computation of the probability of the first-passage time through a given threshold of a stochastic process is a classic problem that appears in many branches of physics. When the stochastic dynamics is markovian, the probability admits…
We develop a recursive method for perturbative solutions of the Fokker-Planck equation with nonlinear drift. The series expansion of the time-dependent probability density in terms of powers of the coupling constant is obtained by solving a…
We explore whether quantum field theory can be understood as the statistical mechanics of a time-reversal-invariant stochastic generalization of Hamiltonian dynamics. The motivation for this project, started with this paper, is to assign…
We present a continuation method that entails generating a sequence of transition probability density functions from the prior to the posterior in the context of Bayesian inference for parameter estimation problems. The characterization of…
An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…
The probability current is a vital quantity in the Fokker-Planck description of stochastic processes. It characterizes non-equilibrium stationary states and appears in linear response calculations. We recover and review the probability…
Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…
We present a framework, which, from the trajectories detailing the spatiotemporal dynamics of a population, simultaneously reconstructs a transport map as well as the Fokker-Planck equation governing the coarse-grained probability…
The time dependence of the survival probability, S(t), is determined for diffusing particles in two dimensions which are also driven by a random unidirectional zero-mean velocity field, v_x(y). For a semi-infinite system with unbounded y…
It is shown that in the complex trajectory representation of quantum mechanics, the Born's Psi^{\star}\Psi probability density can be obtained from the imaginary part of the velocity field of particles on the real axis. Extending this…
The presented explanations are provided for the one--dimensional diffusion process with constant drift by using forward Fokker--Planck technique. We are interested in the outflow probability in a finite interval, i.e. first passage time…
One obtains a probabilistic representation for the entropic generalized solutions to a nonlinear Fokker-Planck equation in $\mathbb R^d$ with multivalued nonlinear diffusion term as density probabilities of solutions to a nonlinear…
It is shown that a normalisable probability density can be defined for the entire complex plane in the modified de Broglie-Bohm quantum mechanics, which gives complex quantum trajectories. This work is in continuation of a previous one that…