#brownian motion #einstein #stochastic

Brown's observations on Brownian motion

In 1828, Robert Brown published the manuscript entitled “A brief account of microscopical observations made in the months of June, July and August 1827, on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies” in the Edinburgh new Philosophical Journal [download it in pdf format here]. He suspended some of the pollen grains of the species Clarkia pulchella in water and examined them closely, only to see them “filled with particles” of around 5 µm diameter that were “very evidently in motion”. He was soon satisfied that the movement “arose neither from currents in the fluid nor form its gradual evaporation, but belonged to the particle itself”. Brown’s work was the first comprehensive observation of a phenomena called Brownian motion which remained unexplained until the beginning of the 20th century by Bachelier and most notably by Einstein in his famous paper in 1905. Brownian motion is the most basic description of the dynamics of a particle, price, etc. under the influence of external noise. ...

#arxiv #finance #preprint #stock market

New section in the arXiv: Quantitative Finance

News from the arXiv: a new section has been created to host preprints about Quantitative Finance. The section (as stated in the press release) intends to fix a problem with existing pre-print repositories. One one hand, social sciences repositories like SSRN, RepEC/IDEAS and others are too academic for practitioners, while on the other hand sites like defaultrisk.com or wilmott.com have not attracted many academic contributors. The new category in the arXiv would be a gathering point for both practitioners and academic people working in this important research field ...

#complexity #game theory #nobel prize

Is Game Theory a scientific theory?

A wonderful quote about the nature of Game Theory Game theory is no doubt wonderful for telling stories. However, it flunks the main test of any scientific theory: The ability to make empirically testable predictions. In most real-life situations, many different outcomes -- from full cooperation to near-disastrous conflict -- are consistent with the game-theory version of rationality. by Michael Mandel, on Kahneman and Smith 2002 Nobel Prize in Economics.  ...

#ito #stochastic differential equation #wiener

Kiyoshi Itô, 93, dies

November was a rather sad month in the world of stochastic differential equations. In the 26th we were suppose to be celebrating the birth of one of the best mathematicians in history, Norbert Wiener, who gives name to the Wiener process, usually denoted W(t). However, in the 10th, Kiyoshi Itô, the father of stochastic differential equations, passed away. Interestingly both are present in a simple stochastic differential equation like this ...