Brownian motion apart once the particle is in motion. Also, there would be a distribution of different possible Δ"V"s instead of always just one in a realistic situation. The diffusion equation yields an approximation of the time evolution of the probability density function associated to the position of the particle going under a Brownian movement under the physical definition. The approximation is valid on short timescales. The time evolution of the position of the Brownian particle itself is best described using Langevin equation, an equation which involves a random force field representing the effect of the thermal fluctuations of the solvent on
Brownian model of financial markets for buying or selling). Another assumption is that asset prices have no jumps, that is there are no surprises in the market. This last assumption is removed in jump diffusion models. Consider a financial market consisting of formula_1 financial assets, where one of these assets, called a "bond" or "money market", is risk free while the remaining formula_2 assets, called "stocks", are risky. A "financial market" is defined as formula_3 that satisfies the following: Let formula_17 be a probability space, and a formula_18 be D-dimensional Brownian motion stochastic process, with the natural filtration: If formula_20 are the measure 0 (i.e.