EXACT SOLUTIONS AND MONTE CARLO SIMULATIONS OF SELF-CONSISTENT LANGEVIN EQUATIONS: A CASE STUDY FOR THE COLLECTIVE DYNAMICS OF STOCK PRICES

2007 ◽  
Vol 21 (07) ◽  
pp. 1099-1112 ◽  
Author(s):  
T. D. FRANK
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Langevin Equation ◽  
Analytical Solutions ◽  
Planck Equation ◽  
Collective Dynamics ◽  
Fokker Planck Equation ◽  
Self Consistent ◽  
Fokker Planck

In a case study, the exact solution of a self-consistent Langevin equation associated with a nonlinear Fokker–Planck equation is derived. On the basis of this solution, a Monte Carlo simulation scheme for the Langevin equation is proposed. The case study addresses a generalized geometric Brownian walk that describes the collective dynamics of a large set of interacting stocks. Numerical results obtained from the Monte Carlo simulation are compared with analytical solutions derived from the nonlinear Fokker–Planck equation. The power of the Monte Carlo simulation is demonstrated for situations in which analytical solutions are not available.

scholarly journals Study of the slowing down of high energy proton shots through metals via a Monte Carlo simulation of the Fokker-Planck equation

2005 ◽  
Vol 20 (2) ◽  
pp. 23-27
Author(s):  
Francesco Teodori ◽  
Vincenzo Molinari
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Planck Equation ◽  
High Energy ◽  
High Energy Proton ◽  
Slowing Down ◽  
Energy Proton ◽  
Fokker Planck Equation ◽  
Multi Body ◽  
Fokker Planck

The aim of this work is to analyze the diffusion and the slowing down of high energy proton shots through a target. Analyzing the phenomenon rigorously with the full transport equations, means tack ling many difficulties, most of which arise from the long range nature of the Coulomb interactions involving more than one particle simultaneously. The commonly used approach of neglecting the multi-body collisions, though correct for rarefied neutral gases, of ten leads to very poor approximations when charged particles moving through dense matter are considered. Here we present a Monte Carlo simulation of the Fokker-Planck equation where the multi-body collisions are taken into account. The model al lows the calculation of a point-wise distribution of energy and momentum transferred to the tar get.

scholarly journals Alignment of Dust Grains by Magnetic Relaxation: A Comparison Between Results Obtained by Two Different Methods

1973 ◽  
Vol 52 ◽  
pp. 187-189
Author(s):  
P. Cugnon
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Magnetic Relaxation ◽  
Planck Equation ◽  
Dust Grains ◽  
Fokker Planck Equation ◽  
The Monte Carlo Method ◽  
Good Agreement ◽  
Fokker Planck

This paper is devoted to a comparison between results obtained by Purcell and Spitzer (1971) using a Monte-Carlo method and by the author (1971) using a Fokker-Planck equation. It is shown that there is a good agreement between the results within the dispersion expected from the Monte-Carlo method.

ON THE MONTE CARLO SIMULATION APPROACH TO FOKKER-PLANCK EQUATIONS IN QUANTUM OPTICS

1994 ◽  
Vol 08 (04) ◽  
pp. 239-246 ◽  
Author(s):  
G.M. D’ARIANO ◽  
C. MACCHIAVELLO ◽  
S. MORONI
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Quantum Optics ◽  
Planck Equation ◽  
Optical Amplifier ◽  
Optical Systems ◽  
Simulation Approach ◽  
Number Representation ◽  
Fokker Planck Equations ◽  
Fokker Planck

The suitability of the Monte Carlo simulation approach to Fokker-Planck equations in quantum optics is investigated. The method is especially useful for multimode analysis, and hence for studying realistic models of nonlinear optical systems. Here it is illustrated on the basis of two simple examples of application: i) a one-dimensional Fokker-Planck equation in the number representation, which describes a simple model of optical amplifier, and ii) the Van der Pol two-dimensional equation in the P-function representation.

scholarly journals Deterministic and Stochastic Research of Cubic Population Model with Harvesting

2021 ◽  
pp. 2150023
Author(s):  
Özgür Gültekin ◽  
Çağatay Eskin ◽  
Esra Yazicioğlu
Keyword(s):  
Langevin Equation ◽  
Allee Effect ◽  
Deterministic Model ◽  
Probability Distributions ◽  
Gaussian White Noise ◽  
Quadratic Function ◽  
Planck Equation ◽  
Detailed Examination ◽  
Fokker Planck Equation ◽  
Fokker Planck

A detailed examination of the effect of harvesting on a population has been carried out by extending the standard cubic deterministic model by considering a population under Allee effect with a quadratic function representing harvesting. Weak and strong Allee effect transitions, carrying capacity, and Allee threshold change according to harvesting are first discussed in the deterministic model. A Fokker–Planck equation has been obtained starting from a Langevin equation subject to correlated Gaussian white noise with zero mean, and an Approximate Fokker–Planck Equation has been obtained from a Langevin equation subject to correlated Gaussian colored noise with zero mean. This allowed to calculate the stationary probability distributions of populations, and thus to discuss the effects of linear and nonlinear (Holling type-II) harvesting for populations under Allee effect and subject to white and colored noises, respectively.

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