Brownian motion in magnetic field: A model for a semi-quantum stochastic process

1981 ◽  
Vol 40 (4) ◽  
pp. 353-357 ◽  
Author(s):  
Amal K. Das
Keyword(s):  
Magnetic Field ◽  
Stochastic Process ◽  
Brownian Motion ◽  
Quantum Stochastic Process

Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

2007 ◽  
Vol 44 (02) ◽  
pp. 393-408 ◽  
Author(s):  
Allan Sly
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
White Noise ◽  
Gaussian Process ◽  
Discrete Data ◽  
Hölder Exponent ◽  
Scaling Properties ◽  
Multifractional Brownian Motion ◽  
Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

scholarly journals Self-exciting multifractional processes

2021 ◽  
Vol 58 (1) ◽  
pp. 22-41
Author(s):  
Fabian A. Harang ◽  
Marc Lagunas-Merino ◽  
Salvador Ortiz-Latorre
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Rate Of Convergence ◽  
Existence And Uniqueness ◽  
Volterra Equation ◽  
The Self ◽  
The Past ◽  
Stochastic Volterra Equation ◽  
Multifractional Brownian Motion ◽  
Self Organizing

AbstractWe propose a new multifractional stochastic process which allows for self-exciting behavior, similar to what can be seen for example in earthquakes and other self-organizing phenomena. The process can be seen as an extension of a multifractional Brownian motion, where the Hurst function is dependent on the past of the process. We define this by means of a stochastic Volterra equation, and we prove existence and uniqueness of this equation, as well as giving bounds on the p-order moments, for all $p\geq1$. We show convergence of an Euler–Maruyama scheme for the process, and also give the rate of convergence, which is dependent on the self-exciting dynamics of the process. Moreover, we discuss various applications of this process, and give examples of different functions to model self-exciting behavior.

Magneto convective flow of casson nanofluid due to Stefan blowing in the presence of bio-active mixers

2021 ◽  
pp. 239779142110166
Author(s):  
Venkatesh Puneeth ◽  
Sarpabhushana Manjunatha ◽  
Bijjanal Jayanna Gireesha ◽  
Rama Subba Reddy Gorla
Keyword(s):  
Magnetic Field ◽  
Brownian Motion ◽  
Convective Flow ◽  
Three Dimensional ◽  
Induced Magnetic Field ◽  
Density Profiles ◽  
Casson Nanofluid ◽  
And Brownian Motion ◽  
Similarity Transformations ◽  
The Mathematical Model

The induced magnetic field for three-dimensional bio-convective flow of Casson nanofluid containing gyrotactic microorganisms along a vertical stretching sheet is investigated. The movement of these microorganisms cause bioconvection and they act as bio-active mixers that help in stabilising the nanoparticles in the suspension. The two forces, Thermophoresis and Brownian motion are incorporated in the Mathematical model along with Stefan blowing. The resulting model is transformed to ordinary differential equations using similarity transformations and are solved using [Formula: see text] method. The Velocity, Induced Magnetic field, Temperature, Concentration of Nanoparticles, and Motile density profiles are interpreted graphically. It is observed that the Casson parameter decreases the flow velocity and enhances the temperature, concentration, and motile density profiles and also it is noticed that the blowing enhances the nanofluid profiles whereas, suction diminishes the nanofluid profiles. On the other hand, it is perceived that the rate of heat conduction is enhanced with Thermophoresis and Brownian motion.

scholarly journals Stochastic Processes with a Particular Type of Variograms

2007 ◽  
Vol 2007 ◽  
pp. 1-5 ◽  
Author(s):  
Chunsheng Ma
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Stochastic Processes ◽  
Series Expansion ◽  
Real Line ◽  
Random Fields ◽  
The Other ◽  
Simple Construction ◽  
The Real ◽  
Line Form

This paper is concerned with a class of stochastic processes or random fields with second-order increments, whose variograms have a particular form, among which stochastic processes having orthogonal increments on the real line form an important subclass. A natural issue, how big this subclass is, has not been explicitly addressed in the literature. As a solution, this paper characterizes a stochastic process having orthogonal increments on the real line in terms of its variogram or its construction. Our findings are a little bit surprising: this subclass is big in terms of the variogram, and on the other hand, it is relatively “small” according to a simple construction. In particular, every such process with Gaussian increments can be simply constructed from Brownian motion. Using the characterizations we obtain a series expansion of the stochastic process with orthogonal increments.

scholarly journals Brownian motion in a magnetic field

2001 ◽  
Vol 63 (2) ◽  
Author(s):  
Radosław Czopnik ◽  
Piotr Garbaczewski
Keyword(s):  
Magnetic Field ◽  
Brownian Motion

Brownian motion of a classical harmonic oscillator in a magnetic field

2008 ◽  
Vol 77 (5) ◽  
Author(s):  
J. I. Jiménez-Aquino ◽  
R. M. Velasco ◽  
F. J. Uribe
Keyword(s):  
Magnetic Field ◽  
Brownian Motion ◽  
Harmonic Oscillator

Entropy generation of nanofluid flow and heat transfer driven through a paralleled microchannel

2019 ◽  
Vol 97 (6) ◽  
pp. 678-691 ◽  
Author(s):  
Hang Xu ◽  
Ammarah Raees ◽  
Xiao-Hang Xu
Keyword(s):  
Magnetic Field ◽  
Brownian Motion ◽  
Entropy Generation ◽  
Current Model ◽  
Entropy Generation Rate ◽  
Physical Parameters ◽  
Nanofluid Flow ◽  
Buongiorno’S Model ◽  
Flow Models ◽  
Flow And Heat Transfer

In this paper, a fully-developed, immiscible nanofluid flow in a paralleled microchannel in the presence of a magnetic field is investigated. Buongiorno’s model is applied to describe the behaviors of the nanofluid flow. Different from most previous studies on microchannel flow, here the pressure term is considered as unknown, which makes the current model compatible with the commonly accepted channel flow models. The influences of various physical parameters on important physical quantities are given. The entropy generation analysis is performed. Variations of local and global entropy generations with the magnetic field parameter, the electric field, and the viscous dissipation parameter under various ratios of the thermophoresis parameter to the Brownian motion parameter are illustrated. The results indicate that the entropy generation rate strongly depends on the thermophoresis and the Brownian motion parameters. Their increase enhances the total irreversibility of entropy generation.

Portfolio choice and the Bayesian Kelly criterion

1996 ◽  
Vol 28 (04) ◽  
pp. 1145-1176 ◽  
Author(s):  
Sid Browne ◽  
Ward Whitt
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Portfolio Choice ◽  
Random Environment ◽  
Continuous Time ◽  
Success Probability ◽  
Simple Random Walk ◽  
Diffusion Limit ◽  
Kiefer Process ◽  
Time Problem

We derive optimal gambling and investment policies for cases in which the underlying stochastic process has parameter values that are unobserved random variables. For the objective of maximizing logarithmic utility when the underlying stochastic process is a simple random walk in a random environment, we show that a state-dependent control is optimal, which is a generalization of the celebrated Kelly strategy: the optimal strategy is to bet a fraction of current wealth equal to a linear function of the posterior mean increment. To approximate more general stochastic processes, we consider a continuous-time analog involving Brownian motion. To analyze the continuous-time problem, we study the diffusion limit of random walks in a random environment. We prove that they converge weakly to a Kiefer process, or tied-down Brownian sheet. We then find conditions under which the discrete-time process converges to a diffusion, and analyze the resulting process. We analyze in detail the case of the natural conjugate prior, where the success probability has a beta distribution, and show that the resulting limit diffusion can be viewed as a rescaled Brownian motion. These results allow explicit computation of the optimal control policies for the continuous-time gambling and investment problems without resorting to continuous-time stochastic-control procedures. Moreover they also allow an explicit quantitative evaluation of the financial value of randomness, the financial gain of perfect information and the financial cost of learning in the Bayesian problem.

Pathwise convergent higher order numerical schemes for random ordinary differential equations

2007 ◽  
Vol 463 (2087) ◽  
pp. 2929-2944 ◽  
Author(s):  
Peter E Kloeden ◽  
Arnulf Jentzen
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Vector Field ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Higher Order ◽  
Time Variable ◽  
Numerical Schemes ◽  
Hölder Continuous ◽  
Usual Order

Random ordinary differential equations (RODEs) are ordinary differential equations (ODEs) with a stochastic process in their vector field. They can be analysed pathwise using deterministic calculus, but since the driving stochastic process is usually only Hölder continuous in time, the vector field is not differentiable in the time variable, so traditional numerical schemes for ODEs do not achieve their usual order of convergence when applied to RODEs. Nevertheless deterministic calculus can still be used to derive higher order numerical schemes for RODEs via integral versions of implicit Taylor-like expansions. The theory is developed systematically here and applied to illustrative examples involving Brownian motion and fractional Brownian motion as the driving processes.

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