Mathematics, Stochastic Modelling, Quantitative Finance, Finance, Probability.
infinitesimal increment of Brownian motion over an infinitesimal time interval 𝑑𝑡. For an infinitesimal time interval dt, the increment dWt​ behaves similarly: 𝑑𝑊𝑡∼𝑁(0,𝑑𝑡). The expectation of the square of this increment is: 𝐸[(𝑑𝑊𝑡)²] = 𝑑𝑡. If we sum up the squared increments over a time interval