From theory to practice - page 282

 
Yuriy Asaulenko:

OK, let's look at the other end. The state of a material point (which is more primitive) is already described by a 16-dimensional vector (if I haven't forgotten)). One dimension is forgotten, and all our calculations are worthless altogether.

And A_K2 - looked at one dimension - no, says the process is non-Markovian.

And I say that a 4-dimensional vector already describes the process quite well and already allows us to get adequate prediction on a short interval for 70% of the test time interval. My old systems (before 14-15 yrs) used this as one of the entry/exit conditions. And where is this non-marking?

6, I was reading today...

 
Renat Akhtyamov:

6, I read today...

Actually, for a mat point there are as many as 19.)) mass, coordinates, velocities, accelerations, forces, moments, moments of inertia.

 
Yuriy Asaulenko:

Actually, for a mat point there are as many as 19.)) mass, coordinates, velocities, accelerations, forces, moments, moments of inertia.


Yura, well, well, well...

You've read all this before, but for some reason you're trying to confuse the tracks...
 
Renat Akhtyamov:

Yura, well, well, well...

You have read it all before, but for some reason you are trying to confuse the traces...

Actually, the accelerations are unnecessary there, but we need to add angular velocities). 19 so far, if I haven't forgotten.

Well, I think I have listed everything, count it.

Even for your case - mass, coordinates, velocities, forces - it's already 10-dimensional to describe the system. Where is 6?

 
Yuriy Asaulenko:

Actually, the accelerations are unnecessary there, but we need to add angular velocities). 19 so far, if I haven't forgotten.

Well, I think I've listed everything, do the math.

Even for your case - mass, coordinates, velocities, forces - it's already 10-dimensional. Where is 6?

I have no words, only letters and they are above, in the penultimate line

Naturally, the explanation is even higher.

But it's water, that's not the point.
 
Renat Akhtyamov:
I have no words, just letters and they're above, in the penultimate line

I don't understand what's unclear? It seems to be even within the limits of a school course.( Ok, let's forget it.

In short, before working with a system, one has to define its state, and it is expressed by a vector. As we have seen, even in the simplest cases with a mat point.

 
Yuriy Asaulenko:

I don't understand what's unclear? It seems to be even within the limits of a school course.( Ok, let's forget it.

In short, before working with a system, one has to define its state, and it is expressed by a vector. As we've seen, even in the simplest cases with a mat point.

is unnecessary, you don't know who I am...

The rest is on point, I might even add - finally.

 
Renat Akhtyamov:

is unnecessary, you don't know who I am...

The rest is spot on, I might even add - finally

By the way, I wonder who? You can write me in person. It would be easier to communicate. I have it in my profile, if it hasn't been torn down in upgrades.

As for market condition, I'm guessing it's somewhere around a 15 dimensional vector. The real dimensionality might be less, but to get rid of noise no less. i.e., you need at least 15 points of history to determine the current state.

 
Yuriy Asaulenko:

By the way, I wonder who? You can write to me in person. It would be easier to communicate. I have it on my profile, if it hasn't been demolished in upgrades.

As for market condition, I assume it's somewhere around a 15 dimensional vector. The real dimensionality may be less, but to get rid of noise no less is possible. i.e. to determine the current state you need at least 15 points of history.

The distribution of the increments is normal, as expected.

So, the process is non-Markovian, as required to prove it !!!


 
Renat Akhtyamov:

I'm sitting here scratching my head..... That can't be right.

The distribution of increments is normal, as expected. But why is it symmetrical, just a copy?

A mistake? :


If the distribution of increments is normal - the process is Wienerian, i.e. stationary and predictable. Lay out the mathematics of the BP transformation - it's the Grail, we'll investigate. We'll divide the dollar cash, no offense.

Reason: