Mnxn is a non-negative real square matrix subject to a statistical condition,
∑Mi,j =1 for all lines i,
or ∑Mi,j =1 for all columns j,
Compared to the double statistical transition matrix B, its uses are limited to a few events such as:
* Predict the number of defective parts in the assembly line,
**Predict what percentage of a company's accounts receivable will become bad debt.
..etc..
While the double statistical transition matrix B can be used for almost all physical and mathematical events.
Markov chains are a pure mathematical model used to present a stochastic process, which has no place for the source term S or boundary conditions b.
We assume that the universe is made up of space, time and energy.
Thus any physical event, whether classical or quantum, can be expressed in PDE1,2 format [1],
dU/dt)partial = α ∇^2 (U) + S. . . . . (1)
U(x,y,z,t+dt) = B. U(x,y,z,t) . . . . . . (2)
and its solution can be presented in the format of equation 3,
U(x,y,z,t)= D(N) . (b+S) + IC. B^N. . . . . (3)
------
1-Useless Mathematics, ResearchGate, IJISRT Journal, September 2024.
Thus any physical event, whether classical or quantum, can be expressed in PDE1 format and its solution can be presented in the format of equation 3.
Note that in the case of a spontaneous Markovian transfer event not driven by the source term S or the boundary conditions b, you must substitute S=0 and b=0 into equation 3 to obtain,
U(t)=IC. B^N. . . . . . . . .(3*)
Equation 3* is the stochastic Markov matrix equation for the eigenvalue λ =1.
- Badges
- Science topic
- Similar topics
- Biological Science
- Histology
- Fixatives