Can somebody help me with working out: $$E[(N_{t}-\lambda t)^2\mid F_{s}]$$ where $N_{t}$ is a Poisson process and $F_{s}$ the $\sigma$-algebra generated by $N_{s}$, $0 \leq s < t$.
2026-03-29 12:31:40.1774787500
Martingale Poisson
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Hint: The (homogeneous) Poisson process has stationary independent increments, so write: $$N_t=N_s+(N_t-N_s)=N_s+N_{t-s}$$ and use that