Related papers: Path probability of stochastic motion: A functiona…
We show the application of an optimal transportation approach to estimate stochastic volatility process by using the flow that optimally transports the set of particles from the prior to a posterior distribution. We also show how to direct…
The run-and-tumble particle (RTP) is one of the simplest examples of an active particle in which the direction of constant motion randomly switches. In the one-dimensional (1D) case this means switching between rightward and leftward…
Experiments on the motion of a particle on an inclined rough plane have yielded some surprising results. For example, it was found that the frictional force acting on the ball is viscous, {\it i.e.} proportional to the velocity rather than…
Subject of this letter is the dynamics of a chain obtained performing the continuous limit of a system of links and beads. In particular, the probability distribution of the relative position between two points of the chain averaged over a…
Transition probabilities for stochastic systems can be expressed in terms of a functional integral over paths taken by the system. Evaluating the integral by the saddle point method in the weak-noise limit leads to a remarkable mapping…
In this paper we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case.…
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…
An extension of the classical action principle obtained in the framework of the gauge transformations, is used to describe the motion of a particle. This extension assigns many, but not all, paths to a particle. Properties of the particle…
We introduce a model for the short-term dynamics of financial assets based on an application to finance of quantum gauge theory, developing ideas of Ilinski. We present a numerical algorithm for the computation of the probability…
In many practically important problems which rely on particles' transport in realistic corrugated channels, one is interested to know the probability that either of the extremities, (e.g., the one containing a chemically active site, or…
Bursty transport phenomena associated with convective motion present universal statistical characteristics among different physical systems. In this letter, a stochastic univariate model and the associated probability distribution function…
A stochastic action principle for stochastic dynamics is revisited. We present first numerical diffusion experiments showing that the diffusion path probability depend exponentially on average Lagrangian action. This result is then used to…
We present a path integral method to derive closed-form solutions for option prices in a stochastic volatility model. The method is explained in detail for the pricing of a plain vanilla option. The flexibility of our approach is…
The integral with respect to a multidimensional stochastic measure, for which we assume only $\sigma$-additivity in probability, is studied. The continuity and differentiability of its realizations are established.
The manner in which probability amplitudes of paths sum up to form wave functions of orbital angular momentum eigenstates is described. Using a generalization of stationary-phase analysis, distributions are derived that provide a measure of…
Observed clusters should be modelled by considering the distribution function to be a random variable that quantifies the degree of excitation of the system's normal modes. A system of canonical coordinates for the space of DFs is…
We derive a stochastic path integral representation of counting statistics in semi-classical systems. The formalism is introduced on the simple case of a single chaotic cavity with two quantum point contacts, and then further generalized to…
Probability is an important question in the ontological interpretation of quantum mechanics. It has been discussed in some trajectory interpretations such as Bohmian mechanics and stochastic mechanics. New questions arise when the…
A numerical experiment of ideal stochastic motion of a particle subject to conservative forces and Gaussian noise reveals that the path probability depends exponentially on action. This distribution implies a fundamental principle…
Recently, progress has been made in the theory of turbulence, which provides a framework on how a deterministic process changes to a stochastic one owing to the change in thermodynamic states. It is well known that, in the framework of…