The market is a controlled dynamic system. - page 109
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It seems a good time to continue the discussion about the nature of dynamic processes. You stopped at the point that a single process is divided into 3 components, linked by a ratio:
Past (P) + Present (H) + Future (B) = 1 process.
Here you had some comments or a "different approach".
And I, having thought about it, am forced to introduce another function : History (I) and present it as a sum of AND = P + H.
Now: History (I) + Future (B) = Past (P) + Present (H) + Future (B) = 1;
Functions I, P, N and B are functions of the same class, are of the same nature, they are transformed by mathematical methods into each other, without violating a logical sequence of occurrence of each of the phases of a single process at the end of a single time, because they have the same "time constant", embodying and revealing the connection of space and time. Isaac Newton was indeed right when he remarked that without a process there is no time and vice versa.
I have my doubts under several circumstances.
1) If the Past is treated as an integral of the Present, i.e. if the Past is a function of the interval F(a,b), then the Present is the differential of that function at the endpoint of the interval -- dF(b). Therefore summation (P+H) is wrong, because it leads to double counting of the Present.
For now we have to decide on this point.
I have doubts in several circumstances.
1) If the Past is treated as an integral of the Present, i.e. if the Past is a function of the interval F(a,b), then the Present is the differential of this function at a finite point of the interval -- dF(b). Therefore summation (P+H) is wrong, because it leads to double counting of the Present.
We have to decide on this point for now.
I'm more confused by the concepts themselves)) How can the past be added to something? Perhaps it makes sense to talk about some function, which may include normalisation, etc. And most importantly to highlight some measurable characteristic of the past and the future. Like:
F(P)+G(B)=1
And try to define somehow F and G. And from the point of view of a task of forecasting it is necessary to find G with known F
I have doubts about several circumstances.
1) If the Past is treated as an integral of the Present, i.e. if the Past is a function of the interval F(a,b), then the Present is the differential of this function at a finite point of the interval -- dF(b). Therefore summation (P+H) is wrong, because it leads to double counting of the Present.
So far we have to decide on this point.
I'm more confused by the concepts themselves.) How does one add up the past to something? Perhaps it makes sense to talk about some function, which may include normalisation, etc. And most importantly to highlight some measurable characteristic of the past and the future. Such as:
F(P)+G(B)=1
And try to define somehow F and G. And from the point of view of a problem of forecasting it is necessary to find G, with known F
Normalising by one is the second point of my doubts.
But if one manages to construct an adequate F(P), then one can get the vector field corresponding to it, and this, in turn, will allow to construct a continuation operator.
The normalization by one is the second point of my doubts.
But if we manage to construct an adequate F(P), we can also get the vector field corresponding to it, and this in turn allows us to construct a continuation operator.
Why hesitate, add up all three functions and get one. Investigate P(t/t) rather than F(P) and see if it is adequate.
Well, if they are constructed based on a normalisation to one, then naturally they will add up to one.
Let us, however, start from the beginning, i.e. from the definition of t,t,n.
And then follow the well-known way: 1) construct a sample function convenient for research; 2) discretize it; 3) from its samples determine t,t,n; 4) from them construct H(t,t,n); 5) then construct P(t,t,n); 6) then construct B(t,t,n); 7) compare the result with the sample function. As a result, we get some sample error. Then we will see what to do with this error.
Neither probability theory nor mathematical statistics are suitable for describing and studying processes in dynamics
I don't really agree with this. There is, for example, a whole theory of random processes passing through linear chains, thick treatises have been written. The nonlinear dynamics of random processes, too, can be found in the literature. It is clear that it is all a combination of matstatistics and other sections, but still.
I do not entirely agree with this. There is, for example, a whole theory of random processes passing through linear circuits, thick treatises are written. Nonlinear dynamics of random processes also appear in the literature. It is clear that it is all a combination of matstatistics and other sections, but still.
There is no need to take the phrase out of context. The context there was completely different.
But for the purpose of clarification, I would add: in its purest form.
Of course, we can use them to determine certain characteristics. But something else needs to be included for further definition.
Let me note in brackets that in order to determine such characteristics or their analogs, we can successfully do without TV and MC in their generally accepted form.
But I am not rejecting TV and MS completely. You just need to understand the limits of their use.
We can successfully do without TV and MC in their usual form.
But I'm not rejecting TV and MS outright. You just have to understand the limits of their use.
delusions of grandeur.
Let's be serious - what do you use for analysis? Don't tell me about controlled dynamic systems - I've read this thread several times and there is not a hint of it here