Brownian model of financial markets as: Note that formula_21 and formula_139 are absolutely continuous with respect to each other, i.e. they are equivalent. Also, according to Girsanov's theorem, is a formula_6-dimensional Brownian motion process on the filtration formula_146 with respect to formula_139. A complete financial market is one that allows effective hedging of the risk inherent in any investment strategy. Let formula_89 be a standard financial market, and formula_149 be an formula_140-measurable random variable, such that: The market formula_89 is said to be "complete" if every such formula_149 is "financeable", i.e. if there is an formula_155-financed portfolio process formula_156, such that its associated wealth process
Brownian ratchet a critical shaking strength. For very strong shaking, the vanes of the paddle wheel interacted with the gas, forming a convection roll, sustaining their rotation. The experiment was filmed. Brownian ratchet In the philosophy of thermal and statistical physics, the Brownian ratchet or Feynman-Smoluchowski ratchet is a thought experiment about an apparent perpetual motion machine first analysed in 1912 by Polish physicist Marian Smoluchowski and popularised by American Nobel laureate physicist Richard Feynman in a physics lecture at the California Institute of Technology on May 11, 1962, during his Messenger Lectures series The Character of Physical Law in Cornell University