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Brownian Motion Markov Property

Medium · Stochastic Calculus · Quant Trader interview question · stochastic-calculus, brownian-motion, markov-property, probability, normal-distribution

Consider a standard Brownian motion $W_t$, where $t \ge 0$. Let $W_s$ represent the value of the Brownian motion at time $s$. According to the Markov property, what can you definitively say about the conditional distribution of $W_t$ given $W_s$ for $t > s$?