Poisson Processes and Brownian Motion
0/102 solvedEach question is graded on a single answer: a check that this chapter's methods work, not a test of the reasoning behind them.
Your answer
About these 102 questions
Counting processes and independent increments; the Poisson process by three equivalent definitions, with arrival times, conditional uniformity, superposition and thinning; compound and non-homogeneous processes; Brownian motion as the random-walk limit, its quadratic variation and roughness; the reflection principle; and renewal and Levy processes. This set covers the chapter Poisson Processes and Brownian Motion in Probability: 30 easy, 49 medium and 23 hard questions, each graded instantly with a hint and a full step-by-step solution. Progress is saved in this browser only.
- Counting processes, increments, and what makes a model tractable — 10 questions
- The Poisson process: three definitions that agree — 11 questions
- Arrival times: exponential gaps and Erlang waits — 10 questions
- Conditional uniformity and the order statistics property — 10 questions
- Superposition, thinning, and marked processes — 10 questions
- Compound and non-homogeneous Poisson processes — 10 questions
- Brownian motion and the random-walk limit — 10 questions
- Path properties: quadratic variation and roughness — 11 questions
- The reflection principle, maxima, and hitting times — 10 questions
- Renewal and Lévy processes: where these two sit — 10 questions
For work on paper there is a printable problem set with separate worked solutions.