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Stochastic Processes

Random walks, Markov chains, SDEs, short-rate models.

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Coupling: one uniform, two processes, pointwise comparison

recommended next

Galton-Watson branching: the criticality threshold

recommend Pólya's urn: exchangeability beats enumeration +3 more first

Markov chains: stationary distributions and long-run fractions

recommend Conditional probability: shrinking the sample space first

Poisson approximation: rare events made mental

recommend Binomial: counting successes in n Bernoulli trials first

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Random walk: gambler's ruin and hitting probabilities

Itô's lemma: where the half-sigma-squared comes from

recommend Random walk: gambler's ruin and hitting probabilities +4 more first

Mean-reverting SDEs: the OU half-life trick

recommend Random walk: gambler's ruin and hitting probabilities +3 more first

Stationarity and invariant measures

recommend Markov chains: stationary distributions and long-run fractions +2 more first

Vasicek short rate: the first closed-form bond price

recommend Mean-reverting SDEs: the OU half-life trick +3 more first

Cointegration: when two non-stationary series share a stationary spread

recommend Stationarity and invariant measures +3 more first

Ergodicity and mixing: why your backtest can quietly lie

recommend Stationarity and invariant measures +2 more first

GARCH: vol clustering and the persistence parameter

recommend Stationarity and invariant measures +3 more first

CIR short rate: no negative rates, by construction

recommend Vasicek short rate: the first closed-form bond price +1 more first

Hull-White: Vasicek that matches today's curve exactly

recommend Vasicek short rate: the first closed-form bond price +1 more first

LMM-SABR: the LIBOR Market Model with SABR vol for rates

recommend Hull-White: Vasicek that matches today's curve exactly +3 more first