Brownian increments

Understanding Brownian motion increments and properties

This is an easy statistics question that tests your familiarity with the foundational properties of standard Brownian motion. It appears frequently in quant interviews because it separates candidates who have internalized the core definitions from those who merely recognize the name.

To solve problems like this, you need to recall two key facts: the distribution of Brownian motion at any fixed time, and the properties of increments over disjoint time intervals. The question combines both a probability calculation and a variance calculation, so it checks whether you can apply these properties accurately under time pressure.

• Marginal distribution of B(t) at a single time point
• Independence and stationarity of Brownian increments
• Scaling properties of variance over time intervals