Level 4: Random walks
Gambler's ruin, hitting probabilities, recurrence, and the reflection principle — the discrete scaffolding under Brownian motion and barrier pricing.
36 problems
First 5 free · rest Premium
- 1→
Gambler's Ruin: Hitting Probability
●●●○○Medium~6 min
- 2→
Gambler's Ruin: Expected Duration
●●●●○Hard~7 min
- 3→
How Far Does a Random Walk Wander?
●●●○○Medium~5 min
- 4→
Bertrand's Ballot Problem
●●●●○Hard~7 min
- 5→
Does the Walk Return Home?
●●●●○Hard~7 min
- 6Premium
Pólya's Theorem: Drunk vs. Drunk Bird
●●●●○Hard~6 min
- 7Premium
Distribution of the Running Maximum
●●●●○Hard~7 min
- 8Premium
The Arcsine Law
●●●●○Hard~6 min
- 9Premium
First Passage for a Biased Walk
●●●●○Hard~7 min
- 10Premium
How Many Sites Does a Walk Visit?
●●●○○Medium~6 min
- 11Premium
Wald's Identity
●●●○○Medium~6 min
- 12Premium
Will Two Random Walkers Meet?
●●●○○Medium~5 min
- 13Premium
Paths That Never Go Negative
●●●●○Hard~7 min
- 14Premium
How Often Back to Zero?
●●●○○Medium~6 min
- 15Premium
Where Is the Walk After n Steps?
●●●○○Medium~5 min
- 16Premium
Duration of a Biased Game
●●●●○Hard~7 min
- 17Premium
Expected Peak of the Walk
●●●●○Hard~6 min
- 18Premium
Why Doubling Doesn't Beat a Fair Game
●●●○○Medium~6 min
- 19Premium
From Random Walk to Brownian Motion
●●●○○Medium~6 min
- 20Premium
Expected Range of a Walk
●●●●○Hard~6 min
- 21Premium
A Walk That Bounces Off the Walls
●●●○○Medium~6 min
- 22Premium
A Surprising Return Identity
●●●●○Hard~7 min
- 23Premium
Return Probability of a Drifting Walk
●●●●○Hard~7 min
- 24Premium
Drawdown of a Random Walk
●●●●○Hard~6 min
- 25Premium
What Is Brownian Motion?
●●●○○Medium~6 min
- 26Premium
Hitting a Level with Drift
●●●○○Medium~6 min
- 27Premium
Quadratic Variation of Brownian Motion
●●●●○Hard~7 min
- 28Premium
Geometric Brownian Motion
●●●●○Hard~7 min
- 29Premium
Probability of Touching a Level
●●●○○Medium~5 min
- 30Premium
First-Passage Time Distribution
●●●●○Hard~7 min
- 31Premium
The Brownian Bridge
●●●●○Hard~7 min
- 32Premium
The Integral of Brownian Motion
●●●○○Medium~6 min
- 33Premium
Mean Reversion: Ornstein–Uhlenbeck
●●●●○Hard~7 min
- 34Premium
The Exponential Martingale
●●●●○Hard~6 min
- 35Premium
Two Correlated Brownian Motions
●●●○○Medium~5 min
- 36Premium
Which Barrier Does BM Hit First?
●●●○○Medium~5 min