RESTful^SOAP web service, briefly

REST stands for Representational State Transfer, this basically means that each unique URL is a representation of some object. You can get the contents of that object using an HTTP GET, use a POST, PUT, or DELETE to modify the object (in practice most of the services use a POST for this).

— soap vs REST (most interviewers probably focus here) —
* REST has only GET POST PUT DELETE; soap uses custom methods “getAge()” etc
* SOAP takes more dev effort, despite it’s name
* SOAP dominates enterprise apps

simplest SDE (not PDE) given by Greg

P91 of Greg Lawler’s lecture notes states that the most basic, simple SDE
  dXt = At dBt     (1)
can be intuitively interpreted this way — Xt is like a process that at time t evolves like a BM with zero drift and variance At2. 

In order to make sense of it, let’s back track a bit. A regular BM with 0 drift and variance_parameter = 33 is a random walker. At any time like 64 days after the start (assuming days to be the unit of time), the walker still has 0 drift and variance_param=33. The position of this walker is a random variable ~ N(0, 64*33). However, If we look at the next interval from time 64 to 64.01, the BM’s increment is a different random variable ~ N(0, 0.01*33).
This is a process with constant variance parameter. In contrast, our Xt process has a … time-varying variance parameter! This random walker at time 64 is also a BM walker, with 0 drift, but variance_param= At2. If we look at the interval from time 64 to 64.01, (due to slow-changing At), the BM’s increment is a random variable ~ N(0, 0.01At2).
Actually, the LHS “dXt” represents that signed increment. As such, it is a random variable ~ N(0, dt At2).

Formula (1) is another signal-noise formula, but without a signal. It precisely describes the distribution of the next increment. This is as precise as possible.

Note BS-E is a PDE not a SDE, because BS-E has no dB or dW term.

filtration without periodic observations

In the stochastic probability (not “statistics”) literature, at least in the beginner level literature, I often see mathematicians elude the notion of a time-varying process. I think they want a more generalized and more rigorous terminology, so they prefer filtration.

I feel most of the time, filtration takes place through time.

Here’s one artificial filtration without a time element — cast a bunch of dice at once (like my story cube) but reveal one at a time.

Fwd: python ctor call syntax

In terms of ctor syntax, I think python is more flexible and less “clean” than java. More like c++.

        return riskgenerator.BasicDealValuationGenerator(envDetails)

Luckily I know BasicDealValuationGenerator is a class in the riskgenerator module, so I know this is likely be calling the ctor.

Stoch Lesson 38 parameters of BM

Lawler defined BM with 2 params – drift and variance v, but the meaning of variance is tricky.

Note a BM is about a TVRV and notice the difference between a N@T vs TVRV. A N@T could be modeled by a Gaussian variable with a variance. The variance v of a BM is about the variance of increment. Specifically, the increment over deltaT is a regular Gaussian RV with a variance = deltaT*v