A probability space of continuous-time discrete value stochastic process with Markov property
Journal Title: JOURNAL OF ADVANCES IN MATHEMATICS - Year 2016, Vol 12, Issue 3
Abstract
Getting acquainted with the theory of stochastic processes we can read the following statement: "In the ordinary axiomatization of probability theory by means of measure theory, the problem is to construct a sigma-algebra of measurable subsets of the space of all functions, and then put a finite measure on it". The classical results for limited stochastic and intensity matrices goes back to Kolmogorov at least late 40-s. But for some infinity matrices the sum of probabilities of all trajectories is less than 1. Some years ago I constructed physical models of simulation of any stochastic processes having a stochastic or an intensity matrices and I programmed it. But for computers I had to do some limitations - set of states at present time had to be limited, at next time - not necessarily. If during simulation a realisation accepted a state out of the set of limited states - the simulation was interrupted. I saw that I used non-quadratic, half-infinity stochastic and intensity matrices and that the set of trajectories was bigger than for quadratic ones. My programs worked good also for stochastic processes described in literature as without probability space. I asked myself: did the probability space for these experiments not exist or were only set of events incompleted? This paper shows that the second hipothesis is true.
Authors and Affiliations
Miloslawa Sokol
Keywords
Related Articles
- EP ID EP651665
- DOI 10.24297/jam.v12i3.519
- Views 138
- Downloads 0
Literal Analytical Solution of Three DimensionalPhotogravitational Circular Restricted Three Body Problem
This paper is devoted to construct the literal analytical solutions in power series form for photogravitationalcircular restricted three body problem in three dimensional space, and taking into account that both primarie...
An Existence Theorem for Quasi-Variational Inequalities
A class of set-valued quasi-variational inequalities is studied in Banach spaces. The concept of QVI was earlier introduced by A. Bensoussan and J. L. Lions [4]. In this paper we give a generalization of the existence th...
Numerical Solutions of Volterra Integral Equation of Second kind Using Implicit Trapezoidal
In this paper, we will be find numerical solution of Volterra Integral Equation of Second kind through using Implicit trapezoidal and that by using Maple 17 program, then we found that numerical solution was highly accur...
( U,R) STRONGLY DERIVATION PAIRS ON LIE IDEALS IN RINGS
Let R be an associative ring , U be a nonzero Lie ideal of R. In this paper , we will present the definition of (U,R) strongly derivation pair (d,g) , then we will get d=0 (resp. g=0 ) under certain conditions on d...
The Continuous Dependence and Numerical Approximation of the Solution of the Quasilinear Pseudo-Parabolic Problem with Periodic Boundary Condition
In this paper we consider a pseudo- parabolic equation with a periodic boundary condition and we prove the stability of a solution on the data. We give a numerical example for the stability of the solution on the data.