Stochastic Processes Interview Questions
This topic is the language of how prices, signals, and events evolve over time. You'll master the four pillars quants live by: Markov chains (where a system settles in the long run), Brownian motion and martingales (the continuous-time backbone of pricing), Ito calculus (the chain rule that's secret
How to think about stochastic processes questions
A stochastic process is randomness unfolding in time, and the problems here reward spotting the structure in that randomness — a memoryless transition, a fair bet, a quantity that's conserved on average — so a forbidding limit becomes a one-line argument.
MARKOV: THE PAST IS A SUMMARY
If the future depends on the present only — not the whole history — the process is Markov, and the entire dynamics live in a transition matrix. Hitting times, stationary distributions, and long-run fractions all reduce to linear algebra on that matrix.
MARTINGALES: FAIR ON AVERAGE
When a process has no drift — its expected next value equals its current one — it's a martingale, and optional stopping lets you equate its value at a clever stopping time to its start. That single identity cracks gambler's-ruin, random-walk, and many “expected time until” problems without summing a series.
The recurring instinct: find the memoryless state or the fair bet hiding in the process, and the long-run question answers itself.
Stochastic Processes questions (40)
- Brownian Motion and the Martingale Property
- Stationarity in Stochastic Processes
- Autocorrelation of Brownian Motion
- Explaining Brownian Motion to a Non-Technical Audience
- Brownian Motion: Covariance, Independent Increments, and Conditional Probability
- Stationary Distribution of a Three-State Markov Chain
- Polya's Urn Model
- Simulating Correlated Brownian Motions via Cholesky
- Markov Chain Steady-State Market Share
- Biased Random Walk Hitting Probability
- Regime-Switching Liquidity: Stationary Distribution and Spell Length
- Coin-Flipping Robot Stationary Distribution
- Gambler's Ruin with Biased Coin
- Optimal Blind Buy Time in a Three-State Process
- Corner Absorption From a 3x3 Center
- HTH vs HH: Which Pattern Appears First?
- Martingale Property of Brownian Motion
- Kalman Filter for a Noisy AR(1) Signal
- Ito's Lemma: Log of Geometric Brownian Motion
- Martingale Stopping Time: Optional Stopping and Expected Duration
- Bayesian Regime Filter for Alpha Signal
- Girsanov's Theorem and the Market Price of Risk
- Brownian Martingale Condition for a Cubic Process
- Hawkes Process Basics
- Computing E[phi(S(t))] via PDE and Monte Carlo
- First-Passage Time of Brownian Motion
- Jump-Robust Volatility Estimation with Bipower Variation
- Robust Kalman Filtering: Handling Outlier Measurements
- Return Probability on a Cayley Tree
- Difference of Geometric Brownian Motions
- Vectorized Heston Model Simulation
- First-Passage Probabilities and Optimal Barriers for Brownian Motion with Drift
- Rauch-Tung-Striebel Smoother in a Local-Level Model
- Absorption Probability on a Finite Random Walk
- Variance of Integrated Brownian Motion
- Brownian Motion, Brownian Bridge, and MCMC for Jump Processes
- Brownian Motion Hitting the Positive Y-Axis
- Meeting Probability on a Grid
- Brownian Motion Exit From an Interval
- Gambler's Ruin with Variable Stakes and the Kelly Criterion
Stochastic Processes interview questions FAQ
What kind of stochastic processes questions show up in quant interviews?
This page collects 40 stochastic processes problems that recur in quant trading and research interviews, each with a full worked solution and the intuition behind it. They range from quick warmups to the harder variants firms use to separate candidates.
How hard are stochastic processes interview questions?
The set spans 4 easy, 15 medium and 21 hard problems. Most sit at medium difficulty — a few minutes of clean reasoning — with a harder tail that rewards knowing the canonical approach rather than grinding.
How should I practice stochastic processes for quant interviews?
Work through them by difficulty, starting just below your level, and write the solution out before checking. 8 are free to open with the full worked solution, so you can judge the quality first. Focus on the recurring patterns rather than memorizing answers — the same handful of ideas generate most variants.
Are these real quant interview questions?
They are a curated set drawn from our problem bank — the kind of stochastic processes question that actually appears in quant interviews, rewritten for clarity with solutions we author ourselves. We don't claim any single wording is verbatim, and every problem carries a full solution.