Take the trivial case where [$]f(Y)=Y[$]. Making your replacement seems to require that 

[$]Y_t - Y_{t-} = E[Y_t - Y_{t-}][$]

But that's generally false. 

NASA Scientists Confirm Water Vapor on Europa


Source: NASA/ESA/K. Retherford/SWRI (link)

If you've been out of the stock market since, let's say, Trump was elected, I can see why you're so grumpy.  I think the stock market would take a hit if Trump were removed from office. But what would really rattle it would be various Warren and/or Sanders tax proposals getting serious consideration...

@Alan "First, as other have pointed out, apparently MSM's are just different language for what are traditionally called "Continuous-time Markov Chains"." Multi-state models mentioned by the OP don't need to be Markov or continuous in time. I wrote that that was the case in medicine (addressed by OP...

The second line looks wrong to me. The first line, which is correct, just adds and subtracts the same expression to an integral w.r.t. [$]dN_t[$]. The differential form of the first line would not contain an [$]E[\cdots][$]. Also, probably a typo on your part, the r.h.s. of the 2nd line should have ...

There is also the popular terminology surrounding burn rates , etc. He makes no mention of this, but it is sort of inherently implied. For example, you receive some capital, and there is some future date at which you must complete your innovation otherwise you will have "burned through" all of your...

Pretty vague. Starting from here , a discrete form might be: [$]r_t = r_{t-1} + \theta_t + \epsilon_t[$], where [$]\epsilon_t \sim N(0,\sigma^2)[$], where '[$]\sim[$]' means "is distributed as".  N(0,v) denotes an (independent) normal distribution at each step with mean-0 and variance [$]v[$]. Final...

I don't know about formal. If a process [$]H_t[$] jumps by [$]\Delta H_t[$] when [$]N_t[$] increases by one, then Ito's differential is just [$]dH_t = \Delta H_t \, dN_t[$], which is the last one.  If the equivalence between [$]dH_t = \Delta H_t \, dN_t[$] and your last one is not clear, take [$]N_{...

I think bearish is on to something here. Certainly Trump was just gently tickling Zelensky over the Biden/Burisma investigations and Zelensky, being a comedian himself, got a good laugh from it. I'm glad we settled that.  

  
Does Elwyn Berlekamp play a prominent role in the book?

Yes, according to the index. I am only on pg 86 and the next chapter starts with him.

Can anybody name anything Trump ever did as president that was against the interest of Putin? Well, with about 3 secs of thought: 1.  U.S. State Department Approves Sale Of Second Batch Of Javelin Missiles To Ukraine 2.  2018 missile strikes against Syria 3.   U.S. Imposes New Sanctions on Russian ...

there must be some more.... The first thing that came to my mind as a possible counter-example was Bernie Madoff. But then googling turned up: Funds sue Deutsche Bank over Bernard Madoff claims deal Getting back on topic, I am enjoying the book. I have already learned one secret to Simons' success ...

Speaking of Waymo, which I was, they are right now doing an AMA over at reddit: link

oops -- it's over already and my question did not get answered! 

It's like learning to play the violin. Ten thousand hours of practice, but then you can rattle through all four seasons in minutes. But 'ukulele is still better. That analogy may be better than you think. When your ten thousand hours does not help me -- and I still have to practice/train the damn t...

Mc Ghee is outrunned, NNs compute today 100 millions times faster than ODE methods !!!
https://arxiv.org/pdf/1910.07291.pdf

 "Generating these (training) data required over 10 days of computer time".