Stochastic Processes Interview Questions
Stochastic processes - random walks, Markov chains, and Brownian motion - are core to quant research. These questions build intuition for how systems evolve under randomness.
This area covers random walks and gambler's ruin, Markov chains and stationary distributions, martingales, Poisson processes, and an introduction to Brownian motion - models for how systems evolve under randomness.
Interview problems often reduce to setting up a recursion or using the right property (memorylessness, the optional-stopping theorem) rather than heavy computation.
82 stochastic processes questions · 39 free to practise now.
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- At least two in the windowEasyProbabilityStochastic ProcessesView →
- Covariance of summed Brownian motionsEasyStochastic ProcessesView →
- Crossing the origin twiceEasyStochastic ProcessesView →
- Landing two above the startEasyStochastic ProcessesView →
- Profit from a favourable stopping gameEasyExpected ValueStochastic ProcessesView →
- Retries under a hard capEasyExpected ValueStochastic ProcessesView →
- Variance of a sum of Brownian motionEasyStochastic ProcessesView →
- Variance of an asymmetric random walkEasyRandom VariablesStochastic ProcessesView →
- Where the arrivals landEasyProbabilityStochastic ProcessesView →
- An ant returning to its cornerMediumExpected ValueStochastic ProcessesView →
- Covariance of a Poisson processMediumStochastic ProcessesView →
- Dice game, up to three rollsMediumExpected ValueStochastic ProcessesView →
- Dice payoff via WaldMediumExpected ValueStochastic ProcessesView →
- Expected flips for HHMediumRandom VariablesExpected ValueView →
- Expected flips for HHTMediumExpected ValueStochastic ProcessesView →
- Expected flips for HTMediumExpected ValueStochastic ProcessesView →
- First passage to ±1MediumStochastic ProcessesView →
- Gambler's ruinMediumProbabilityStochastic ProcessesView →
- Gambler's ruin (unfair)MediumProbabilityStochastic ProcessesView →
- Is W(t)³ a martingale?MediumStochastic ProcessesView →
- Log-dynamics of a geometric Brownian motionMediumStochastic ProcessesView →
- Norm of a doubly-stochastic stationary vectorMediumLinear AlgebraStochastic ProcessesView →
- The SDE of the reciprocalMediumStochastic ProcessesView →
- Tuning an exponential random walkMediumProbabilityStochastic ProcessesView →
- Variance of a Brownian combinationMediumStochastic ProcessesView →
- Variance of a time-weighted Itô integralMediumCalculusStochastic ProcessesView →
- Variance of integrated Brownian motionMediumStochastic ProcessesView →
- A 12 before two 7sHardProbabilityStochastic ProcessesView →
- Conditioning a Brownian bridgeHardStochastic ProcessesView →
- Hitting zero on a ringHardProbabilityStochastic ProcessesView →
- Laplace transform of a Brownian exit timeHardStochastic ProcessesView →
- Making a power of Brownian motion a martingaleHardStochastic ProcessesView →
- Mean of a mean-reverting processHardStochastic ProcessesFinance & DerivativesView →
- Quadratic variation in mean-squareHardStochastic ProcessesView →
- Second moment of a Gaussian-kernel stochastic integralHardCalculusStochastic ProcessesView →
- The leap-frog's favorite landing spotHardProbabilityStochastic ProcessesView →
- Two Brownian values, both positiveHardProbabilityStochastic ProcessesView →
- Variance of an Itô integralHardStochastic ProcessesView →
- When a power of the process is a submartingaleHardProbabilityStochastic ProcessesView →
- A mean-reverting processMediumStochastic ProcessesFinance & Derivatives Premium
- A stationary probabilityMediumStochastic Processes Premium
- A two-step transitionMediumStochastic Processes Premium
- Absorption probability on a lineMediumProbabilityStochastic Processes Premium
- Arrivals before the rival streamMediumProbabilityStochastic Processes Premium
- Buyer count in a thinned arrival streamMediumProbabilityStochastic Processes Premium
- Conditioning Brownian motion on its futureMediumStochastic Processes Premium
- Expected duration of a fair gameMediumExpected ValueStochastic Processes Premium
- Expected exponential of Brownian motionMediumStochastic Processes Premium
- Expected rolls for two sixes in a rowMediumExpected ValueStochastic Processes Premium
- Expected steps to first reach a levelMediumProbabilityStochastic Processes Premium
- Expected value of a mean-reverting processMediumStochastic Processes Premium
- HT before HH in coin flipsMediumProbabilityStochastic Processes Premium
- Is the random walk squared a martingale?MediumExpected ValueStochastic Processes Premium
- Periodicity and limiting distributionMediumStochastic Processes Premium
- Reaching the target before ruinMediumStochastic Processes Premium
- Renewal-reward fraction of time runningMediumExpected ValueStochastic Processes Premium
- Return time from a three-state chainMediumStochastic Processes Premium
- Risk-neutral up probabilityMediumStochastic ProcessesFinance & Derivatives Premium
- Short-rate modelsMediumStochastic ProcessesFinance & Derivatives Premium
- Splitting a merged Poisson totalMediumStochastic Processes Premium
- Stationary distribution of a two-state chainMediumProbabilityStochastic Processes Premium
- The Markov propertyMediumStochastic Processes Premium
- Variance of a stochastic integralMediumProbabilityStochastic Processes Premium
- Variance of an aggregate Poisson totalMediumRandom VariablesStochastic Processes Premium
- Amoeba extinctionHardProbabilityStochastic Processes Premium
- Branching process extinction (critical)HardProbabilityStochastic Processes Premium
- Branching process extinction (supercritical)HardProbabilityStochastic Processes Premium
- Drunk man on a bridgeHardExpected ValueStochastic Processes Premium
- Ehrenfest urn stationary distributionHardProbabilityStochastic Processes Premium
- Expected duration of a fair walkHardExpected ValueStochastic Processes Premium
- Expected flips for HHHHardExpected ValueStochastic Processes Premium
- Expected flips for HTHHardExpected ValueStochastic Processes Premium
- Expected revisits of the start stateHardExpected ValueStochastic Processes Premium
- Exponential martingale compensatorHardCalculusStochastic Processes Premium
- Four heads in a rowHardExpected ValueStochastic Processes Premium
- Making change in lineHardCombinatoricsStochastic Processes Premium
- Optional stopping between +3 and −5HardExpected ValueStochastic Processes Premium
- Quadratic variation of a scaled Itô integralHardCalculusStochastic Processes Premium
- Reflected paths ending below the levelHardProbabilityStochastic Processes Premium
- Reflecting wall first-passage timeHardExpected ValueStochastic Processes Premium
- Repainting balls to one colorHardExpected ValueStochastic Processes Premium
- World Series bettingHardExpected ValueStochastic Processes Premium
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Frequently asked questions
- What stochastic-processes topics do quant interviews cover?
- Random walks and gambler's-ruin problems, Markov chains and stationary distributions, martingales and optional stopping, Poisson processes, and basic Brownian motion. These are most common in quant-research interviews.
- How do I solve 'expected time' random-walk problems?
- Condition on the first step to set up a recurrence, or use a martingale and the optional-stopping theorem. Recognising which tool fits comes from practising many variants.
- Are stochastic processes needed for trading roles?
- Less than for research roles. Traders should know random walks and basic Markov ideas; deep stochastic calculus is mainly a quant-research and derivatives-pricing expectation.