Mathematics, Stochastic Modelling, Quantitative Finance, Finance, Probability.
increments. 𝑊𝑡​ has normally distributed increments: 𝑊𝑡−𝑊𝑠∼𝑁(0,𝑡−𝑠) for 0 ≤ 𝑠 <𝑡 . 𝑊𝑡​ has continuous paths. Increments: For any time t and small increment Δ𝑡, the increment Δ𝑊𝑡=𝑊(𝑡+Δ𝑡)−𝑊(𝑡) is normally distributed with mean 0 and variance Δt: Δ𝑊𝑡∼𝑁(0,Δ𝑡) Qudratic Variation A snapshot from the book