Poisson Process: dynamics, probability, and alternative characterisations

Introduces the Poisson process, and discusses its various characterisations. Contents by timeline below:

00:31 - Usual definition of Poisson process
01:30 - Poisson paths visualisation (RCLL, cadlag)
06:25 - Derivation of Kolmogorov /Master Equation
15:23 - Solution of Kolmogorov to get Poisson density
21:48 - Poisson in infinitesimal terms (inc infinitesimal generator)
22:37 - Poisson as exponentially distributed waiting times
25:50 - Summary of definitions
26:17 - Poisson as limit of Bernoulli trials

[Zorothustra]

Wow, this is something beyond my expectation, well done! Really appreciate your effort!

[henrikswedish]

Thank you, very nice first (?) presentation of the Poisson. I hope more to follow

[mikiallen]

thanks, sir, would you explain to us if possible in a separate tutorial how one should go about understanding then statistically testing on real data the difference between reversible versus non-reversible jumps ? and under which situation one should choose one model over the other ?
thanks

[djsocialanxiety]

One question I have is at 15:12: If I remember correctly the rows of the generator matrix should not just here, but also in general sum up to zero right? What is the reason behind it? My guess would be it has to do something that the probabilitys need to sum up tone one.

[HarpreetSingh-kezk]

Did I miss to hear "Almost surely" property associated with Levy-processes?

[junwang]

Are you going to talk about the jump diffusion model with stochastic volatility?

[madaragrothendieckottchiwa]

I love mathematics quantpie in the best !!!

[junwang]

8:54, is the small o term should be function of delta t or delta t square?

[sirknightartorias]

See your content is good. Of the high quality. It is just that your presentation is not rendering the content in a manner it should be. You have a very monotonous voice and seems to be very less modulated and looks like you forget to pause a little here and there. Also you could've used a pointer to highlight the points you would be talking about. I know me telling this seems unnecessary, since you may have already addressed this to a specific audience, but since the comments were public, I thought giving you a heads up. Good day.