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Topic: Brownian motion

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Geometric Brownian motion

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Wiener process

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Markov property

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	Brownian Motion (Wiener Process)
		Brownian motion is a simple continuous stochastic process that is widely used in physics and finance for modeling random behavior that evolves over time.
		Brownian motion gets its name from the botanist Robert Brown (1828) who observed in 1827 how particles of pollen suspended in water moved erratically on a microscopic scale—first moving in one direction and then zig zagging in another.
		The motion was caused by water molecules randomly buffeting the particle of pollen.
	www.riskglossary.com /articles/brownian_motion.htm (0 words)

	Brownian motion Summary (Site not responding. Last check: 2007-11-07)
		Brownian motion is the incessant random motion exhibited by microscopic particles immersed in a fluid.
		The Brownian motion of particles in a liquid is due to the instantaneous imbalance in the force exerted by the small liquid molecules on the particle.
		Brownian motion is related to the random walk problem and it is generic in the sense that many different stochastic processes reduce to Brownian motion in suitable limits.
	www.bookrags.com /Brownian_motion (3825 words)

	Brownian motion - Wikipedia, the free encyclopedia
		Brownian motion is among the simplest stochastic processes on a continuous domain, and it is a limit of both simpler (see random walk) and more complicated stochastic processes.
		The Brownian motion of particles in a liquid is due to the instantaneous imbalance in the force exerted by the small liquid molecules on the particle.
		Brownian motion is related to the random walk problem and it is generic in the sense that many different stochastic processes reduce to Brownian motion in suitable limits.
	en.wikipedia.org /wiki/Brownian_motion (1641 words)

	NationMaster - Encyclopedia: Fractional Brownian motion (Site not responding. Last check: 2007-11-07)
		Fractional Brownian motion was initially used in the modelization of hydrological phenomena.
		Brownian noise has long been recognised as one form of unavoidable interference in the transmission of information, while the estimation of floods is a rather recent discovery that is applicable to the environment.
		Brownian noise in this case is caused by the thermal agitation of the molecules of the fluid medium surrounding the diaphragm.
	www.nationmaster.com /encyclopedia/Fractional-Brownian-motion (615 words)

	NationMaster - Encyclopedia: Brownian motion (Site not responding. Last check: 2007-11-07)
		All three quoted examples of Brownian motion are cases of this: In the mathematics of probability, a stochastic process is a random function.
		The Brownian ratchet is a thought experiment about an apparent perpetual motion machine postulated by Richard Feynman in a physics lecture at the California Institute of Technology on May 11, 1962 as an illustration of the laws of thermodynamics.
		In the end, the Brownian motion of particles in a liquid is due to the instantaneous unbalance in the force exerted by the small liquid molecules on the particle.
	www.nationmaster.com /encyclopedia/Brownian-motion (3623 words)

	Brownian motion
		Brownian motion, stochastic motion of a particle suspended in a surrounding gas or liquid of other particles, molecules or atoms, which is in thermodynamical equilibrium.
		The motion of the particle is due to the collisions with the particles from its surrounding and as such is 'random', i.e.
		Brownian motion is often used in nanoscience as a term which should exemplify the 'blind' nature of thermodynamics - the equilibrium thermodynamics cannot 'guide' assembly of particles.
	nanoatlas.ifs.hr /brownian_motion.html (181 words)

	Applications of Brownian Motion (Site not responding. Last check: 2007-11-07)
		Brownian motion is a sophisticated random number generator, based on a process discovered in plants(R. Brown; 1827) This continuous random motion of solid microscopic particles when suspended in a fluid medium is due to the consequence of continuous bombardment by atoms and molecules.
		The explanation of Brownian motion, given by Einstein in 1905 and based on the kinetic-molecular conception of matter, is considered one of the fundamental pillars supporting atomism in its victorious struggle against phenomenological physics in the early years of this century.
		Brownian motion has desirable mathematical characteristics, where statistics can be estimated with great precision, and probabilities can be calculated, and hence scientists and analysts often turn to such an independant process when faced with the analysis of a multidimensional process of unknown origin (ie.
	www.doc.ic.ac.uk /~nd/surprise_95/journal/vol1/skh1/article1.html (1070 words)

	Brownian motion under the microscope
		Their experiment tracked the Brownian fluctuations of a single particle at microsecond time scales and nanometer length scales, marking the first time that single micron-sized particles suspended in fluid have been measured with such high precision.
		A hundred years ago, Einstein first quantified Brownian motion, showing that the irregular movement of particles suspended in a fluid was caused by the random thermal agitation of the molecules in the surrounding fluid.
		Their results validate the corrected form of the equation describing Brownian motion, and underline the fact that deviations from the standard theory become increasingly important at very small time scales.
	www.eurekalert.org /pub_releases/2005-10/epfd-bmu100705.php (0 words)

	Brownian Motion ...............
		Brownian Motion is the erratic and constant movement of tiny particles when they are suspended in a fluid or gas.
		Futher experiments by Brown and others showed that the motion became more rapid and the particles moved farther in a given time interval when the temperature of the water was raised, when the viscosity of the fluid was lowered, or when the size of the particles was reduced.
		The motion of the molecules of the fluid, due to the fact that the fluid contains heat, causes the molecules to strike the suspended particles at random.
	www.worsleyschool.net /science/files/brownian/motion.html (548 words)

	Brownian motion (Site not responding. Last check: 2007-11-07)
		Brownian motion is the simplest stochastic process on acontinuous domain, and it is a limit of both simpler (see random walk) and more complicated stochastic processes.
		Brownian motion is related to the random walk problem and it is generic in the sense that many different stochasticprocesses reduce to Brownian motion in suitable limits.
		The accompanying equation of motion is called the Langevin equation or the Fokker-Planck equation depending on whether it is formulated in terms of random trajectories orprobability densities.
	www.therfcc.org /brownian-motion-25463.html (564 words)

	Brownian motion (Site not responding. Last check: 2007-11-07)
		Mathematically Brownian motion is a Wiener process in which the conditional probability distribution the particle's position at time t +d t given that its position at time t is p is a normal distribution with a mean of p +μ dt and a variance of σ
		The accompanying equation of motion is the Langevin equation or the Fokker-Planck equation depending on whether it is formulated terms of random trajectories or probability densities.
		The theory of Brownian motion is ubiquitous in physics and mathematics, and has recently become very important in mathematical finance and network modeling.
	www.freeglossary.com /Brownian_movement (873 words)

	Applications of Brownian Motion - 2 (Site not responding. Last check: 2007-11-07)
		For the purpose of classification, a normalised fractional Brownian motion feature vector was defined from this estimation concept(not discussed here) to represent the statistical features of the image surface.This was calculated for five different ultrasonic image surfaces.
		It is claimed that this motion, in turn, creates background noise that sets a limit to the lowest pressure resolvable by the sensor, apart from other electrical noise sources that are present in the circuitry.
		Brownian model should also be very useful for the Uncertainty Theory which has been developing extensively in the late 20th century.
	www.doc.ic.ac.uk /~nd/surprise_95/journal/vol2/ykl/article2.html (1576 words)

	Brownian Motion - The Research Goes On ... (Site not responding. Last check: 2007-11-07)
		Brownian motion is a sophisticated random number generator, based on a process in plants discovered by Robert Brown in 1827(Figure 1).
		The 'Elementary theory of Brownian motion' is one of the major investigations by Einstein on the Brownian movement theory in 1908.
		Hence, Brownian motion will remain a strong research area in the coming days, and it is certainly not going to become obsolete in the scientific world, where new technologies are constantly being developed to replace the old ones.
	www-dse.doc.ic.ac.uk /~nd/surprise_95/journal/vol4/ykl/report.html (6808 words)

	Mac Brownian Motion
		Brownian Motion is exhibited in a variety of situations, including motion of particles.
		I hope this will make Brownian Motion, which lies at the heart of a lot of scientific and economic modeling, a little more accessible to people who have not the time or the patience to learn the nuts and bolts of stochastic analysis.
		Fractional Brownian motion was pulled because the algorithm I was using had a bug somewhere that is a devil to track down.
	homepage.mac.com /johnj1/macbm.html (722 words)

	Brownian_motion
		The origin of the motion is at [0,0] and the x and y components of each step are independently and normally distributed with variance 2 and mean 0.
		The mathematical model posits motion in which the steps are not discrete.
		The first to give a theory of Brownian motion was Louis Bachelier in 1900 in his PhD thesis "The theory of speculation", but it was Albert Einstein's independent solution of the problem in his 1905 paper that brought the solution to the attention of physicists.
	www.brainyencyclopedia.com /encyclopedia/b/br/brownian_motion.html (1546 words)

	Brownian motion in metal (Site not responding. Last check: 2007-11-07)
		That is, in Brownian motion, the magnitude of any bounces in one direction will eventually be offset by bounces in other directions, true for all directions.
		A scatterplot of the motion of a molten lead particle in solid aluminum shows that the distance and direction of each displacement, measured at intervals of one-thirtieth of a second, are randomly distributed about the graph's origin.
		Brownian motion in the plane is peculiar in that its fractal dimension is 1.5, exactly halfway between a one-dimensional line and a two-dimensional plane.
	www.lbl.gov /Science-Articles/Archive/MSD-Brownian-motion.html (1109 words)

	Two and one dimensional Brownian motion (Site not responding. Last check: 2007-11-07)
		Brownian motion originally refers to the random motion observed under microscope of a pollen immersed in water.
		On the right, a 1 dimensional Brownian Motion is plotted (just the y position on the 2 dim picture plot against time).
		After a while, the Brownian motion will probably be outside of the square (in fact, almost surely).
	www.ms.uky.edu /~mai/java/stat/brmo.html (235 words)

	Brownian motion
		Brownian motion is the observed movement of small particles as they are randomly bombarded by the molecules of the surrounding medium.
		Brownian motion explains processes as diverse as diffusion of a salt in water and conduction of heat.
		Individual salt ions dissolve and are subject to brownian motion.
	www.math.utah.edu /classes/217/assignment.04.html (967 words)

	Brownian Motion (Site not responding. Last check: 2007-11-07)
		Brownian motion - it is heat motion of smallest particles, weighted in liquid or gas.
		Brownian particles move under the influence of collisions of molecules.
		Molecular-kinetic theory of Brownian motion was developed by A. Einstein (1905).
	library.thinkquest.org /27948/brownian.html (129 words)

	Backgammon, doubling the stakes, and Brownian motion
		This random motion is due to the fact that small particles (that is, water molecules) hit the pollen randomly.
		Brownian motion was first studied as a mathematical object by Bachelier (1900) in the theory of stock markets and by Einstein (1905) to verify the molecular theory of heat.
		So a Brownian motion started at 1/2, and stopped when it hits 0 or 1, is a reasonable model for the evolution of winning chances.
	plus.maths.org /issue15/features/doubling (2960 words)

	A Non-Technical Introduction to Brownian Motion (Site not responding. Last check: 2007-11-07)
		This column introduces the concept of Brownian motion, which has a long history in the physical sciences and a surprisingly long history in the field of finance.
		This phenomenon came to be known as Brownian Motion.
		Brownian motion as a basis for modeling assets on which options trade was evidently discovered by the French doctoral student Louis Bachelier in 1900.
	www.fenews.com /fen42/teach_notes/teaching-notes.html (1719 words)

	Brownian motion (Site not responding. Last check: 2007-11-07)
		The intensity of this chaotic motion is increased with an increase in temperature.
		The main physical principle of Brownian motion is that the mean kinetic energy of any molecule of a liquid (or gas) is equal to the mean kinetic energy of a particle suspended in this ambience.
		Observing the Brownian motion under a microscope, the French physicist J.Perren (1870-1942) measured the Boltzman constant and Avogadro number, which proved to correspond well with the values of these constants found by other methods.
	physics.nad.ru /Physics/English/brow_txt.htm (226 words)

	Penn physicists track the random walks of ellipsoids, test 'lost' theory of Brownian motion
		Brownian motion, the tiny random movements of small objects suspended in a fluid, has served as a paradigm for concepts of randomness ranging from noise in light detectors to fluctuations in the stock market.
		"Brownian motion arises from the aggregate effect of the random collisions of many molecules with suspended objects.
		For example, in one second, the largest number of particles will stay very close, say within one micron, of their starting point; a smaller number will move between one micron and two microns; a still smaller number will move between two microns and three microns, and so on.
	www.eurekalert.org /pub_releases/2006-10/uop-ppt102506.php (0 words)

	Einstein on Brownian Motion (Site not responding. Last check: 2007-11-07)
		And still another is the paper on the so-called Brownian Motion which encouraged Jean Perrin to pursue his experimental work for confirming the kinetic theory and showing the existence of atoms.
		In this paper it will be shown that, according to the molecular-kinetic theory of heat, bodies of a microscopically visible size suspended in liquids must, as a result of thermal molecular motions, perform motions of such magnitudes that they can be easily observed with a microscope.
		It is possible that the motions to be discussed here are identical with so-called Brownian molecular motion; however, the data available to me on the latter are so imprecise that I could not form a judgment on the question.
	www.bun.kyoto-u.ac.jp /~suchii/einsteinBM.html (682 words)

	Robert Brown, originator of Brownian movement and the cell nucleus, in research by Brian J Ford.
		The analysis of Brownian movement by A. Einstein in 1905 led to the formulation of the Boltzmann Constant, and shortly afterwards J. Perrin began his publications in Paris.
		To this day the nature of Brownian movement is debated, and its cause still argued; the mathematics of the phenomenon continues to occupy a significant tranche of contemporary publications in physics.
		But this qualification is unnecessary to any seasoned microscopist: Brownian movement is instantly recognisable for what it is. The size of particles within the pollen was hard to estimate, though a working diameter of approximately 2µm could be offered.
	www.brianjford.com /wbbrowna.htm (2994 words)

	MICROSCOPY UK / MICSCAPE - Microscopy around the home, studying Brownian motion
		This demonstrates an important feature of classical Brownian motion; the random molecular bombardment giving rise to the motion is responsible for diffusion.
		He was studying the fertilisation process in the plant Clarkia pulchella when he noticed the motion in tiny particles suspended within the medium of living pollen grains.
		It was not until later in the 19th century that correct physical explanations of the motion were formulated and Brownian motion was historically one of the first direct pieces of evidence for the existence of molecules.
	www.microscopy-uk.org.uk /dww/home/hombrown.htm (0 words)

	fractional Brownian motion (Site not responding. Last check: 2007-11-07)
		Fractional Brownian motion is also known as the "Random Walk Process." It basically consists of steps in a random direction and with a step-length that has some characteristic value.
		In other words Brownian Motion is a line that will jump up and down a random amount and simular to the "How Long is the Coast of Britain?" problem, as you zoom in on the function you will discover similar patterns to the larger function.
		The main difference between fBm and regular Brownian motion is that while the increments in Brownian Motion are independent they are dependent in fBm.
	davis.wpi.edu /~matt/courses/fractals/brownian.html (328 words)

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