Are the sample paths of Brownian Motion differentiable? Briefly explain.
Tags
First, understand the nature of Brownian Motion: it's a continuous-time stochastic process characterized by its randomness and noisiness. You'll need to be familiar with the concepts of differentiability and continuity in the context of stochastic calculus. Note that rigorous proofs often involve technical details from measure theory and stochastic analysis, but you can approach this question qualitatively by considering the properties of Brownian paths: their erratic, non-smooth behavior and how they change over infinitesimally small intervals.
Companies Asking this quesiton.
Hard Difficulty
Hard questions require advanced understanding and critical thinking. Here, your problem-solving skills are key, as these questions often involve complex scenarios needing in-depth analysis and well-structured responses.
Technical question
Technical questions probe into your industry-specific knowledge and skills. They require precise answers and are an opportunity to show your expertise and practical abilities in your field.