Brownian motion diverges as the window shrinks, thus rendering the calculation a singular perturbation problem. Brownian motion Brownian motion or pedesis (from "leaping") is the random motion of particles suspended in a fluid (a liquid or a gas) resulting from their collision with the fast-moving molecules in the fluid. This pattern of motion typically alternates random fluctuations in a particle's position inside a fluid sub-domain with a relocation to another sub-domain. Each relocation is followed by more fluctuations within the new closed volume. This pattern describes a fluid at thermal equilibrium, defined by a given temperature. Within such fluid there exists no
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.