- #1
ssyldy
- 4
- 0
Hey guys, I encounter a question (maybe a silly one )that puzzles me. Nt is a Poisson process and λ is the jump intensity.Since the quadratic variation of Poisson process is [N,N]t=Nt, and Nt2-[N,N]t is a martingale, it follows that E[Nt2]=E[[N,N]t]=λ*t. On the other hand, the direct calculation of E[Nt2] can be found in https://proofwiki.org/wiki/Variance_of_Poisson_Distribution, which indicates E[Nt2]=(t*λ)2+t*λ. The two results are different. I really appreciate it if somebody can help me.
Last edited: