Related papers: Stochastic Methods and Dynamical Wave-function Col…
A stochastic approach is implemented to address the problem of a marine structure exposed to water wave impacts. The focus is on (i) the average frequency of wave impacts, and (ii) the related probability distribution of impact kinematic…
Stochastic processes are proposed whose master equations coincide with classical wave, telegraph, and Klein-Gordon equations. Similar to predecessors based on the Goldstein-Kac telegraph process, the model describes the motion of particles…
A conceptual model for microscopic-macroscopic slow-fast stochastic systems is considered. A dynamical reduction procedure is presented in order to extract effective dynamics for this kind of systems. Under appropriate assumptions, the…
Energy nonconservation is a serious problem of dynamical collapse theories. In this paper, we propose a discrete model of energy-conserved wavefunction collapse. It is shown that the model is consistent with existing experiments and our…
Stochastic models for pore collapse in granular materials are developed. First, a general fluctuating stress-strain relation for a plastic flow rule is derived. The fluctuations account for non-associativity in plastic deformations…
Almost a century after the development of quantum mechanics, we still do not have a consensus on the process of collapse of wavefunctions. Some theories require the intervention of a conscious observer while some see it as a stochastic…
A tutorial review is given of some developments and applications of stochastic processes from the point of view of the practicioner physicist. The index is the following: 1.- Introduction 2.- Stochastic Processes 3.- Transient Stochastic…
The basic strategy underlying models of spontaneous wave function collapse (collapse models) is to modify the Schroedinger equation by including nonlinear stochastic terms, which tend to localize wave functions in space in a dynamical…
Instability-induced random branching of deterministic dynamics is discussed as a possible mechanism of random wave function collapse. In the case of two level systems, the Born probability rule emerges as the simplest linear solution to the…
Several methods of statistical analysis are proposed and analyzed in application for a specific task -- extraction of the structure functions from the cross sections of deep inelastic interactions of any type. We formulate the method based…
Stochastic processes associated with traveling wave solutions of the sine-Gordon equation are presented. The structure of the forward Kolmogorov equation as a conservation law is essential in the construction and so is the traveling wave…
The assumption that wave function collapse is induced by correlating interactions of the kind that constitute measurements leads to a stochastic collapse equation that does not require the introduction of any new physical constants and that…
Lagrangian stochastic methods are widely used to model turbulent flows. Scarce consideration has, however, been devoted to the treatment of the near-wall region and to the formulation of a proper wall-boundary condition. With respect to…
A picture of dynamical collapse of the wave function which is relativistic and time symmetric is presented. The part of the model which exhibits these features is the set of collapse outcomes. These play the role of matter distributed in…
We consider stochastic volatility models using piecewise constant parameters. We suggest a hybrid optimization algorithm for fitting the models to a volatility surface and provide some numerical results. Finally, we provide an outlook on…
This paper exposes a novel exploratory formalism, which end goal is the numerical simulation of the dynamics of a cloud of particles weakly or strongly coupled with a turbulent fluid. Giventhe large panel of expertise of the list of…
We consider minimization of stochastic functionals that are compositions of a (potentially) non-smooth convex function $h$ and smooth function $c$ and, more generally, stochastic weakly-convex functionals. We develop a family of stochastic…
An introduction to the CSL (Continuous Spontaneous Localization) theory of dynamical wave function collapse is provided, including a derivation of CSL from two postulates. There follows applications to a free particle, or to a `small' rigid…
Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…
This paper provides convergence analysis for the approximation of a class of path-dependent functionals underlying a continuous stochastic process. In the first part, given a sequence of weak convergent processes, we provide a sufficient…