It was established in the first half of the twentieths century that Brownian motion (Wiener process) \(B\left ( s\right ) \) is of fundamental importance for stochastic modeling of many real life processes ranging from diffusion of pollen on a water surface to volatility of financial markets. Further development of stochastic modeling broughtup more complicated mathematical tools, including integrals with respect to Brownian motion.

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ITÔ Integral

  • Boris L. Rozovskiı̆

摘要

It was established in the first half of the twentieths century that Brownian motion (Wiener process) \(B\left ( s\right ) \) is of fundamental importance for stochastic modeling of many real life processes ranging from diffusion of pollen on a water surface to volatility of financial markets. Further development of stochastic modeling broughtup more complicated mathematical tools, including integrals with respect to Brownian motion.