TL;DR
A stochastic process where the future state depends only on the current state, not the history: \( P(X_{n+1}|X_n, X_{n-1}, \ldots) = P(X_{n+1}|X_n) \). This is the Markov property.
Markov Chain
A stochastic process where the future state depends only on the current state, not the history: \( P(X_{n+1}|X_n, X_{n-1}, \ldots) = P(X_{n+1}|X_n) \). This is the Markov property.
Why it matters for interviews
Markov chains model credit rating transitions, regime-switching models, and order book dynamics. Interview questions often involve computing absorption probabilities, stationary distributions, or expected hitting times.
Definition and Mathematical Foundation
A stochastic process where the future state depends only on the current state, not the history: \( P(X_{n+1}|X_n, X_{n-1}, \ldots) = P(X_{n+1}|X_n) \). This is the Markov property.
Application in Quantitative Finance
Markov chains model credit rating transitions, regime-switching models, and order book dynamics. Interview questions often involve computing absorption probabilities, stationary distributions, or expected hitting times.
Related Terms
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