Abstract
The processes of interaction of microlevel stochatsic elements are modeled by solving the n-dimensional controlled stochastic Ito equation (given in the random process theory [1] with regular limitations), which is considered as an initial object: where U t is the n-dimensional Wiener’s process, C=C(Δ, R n) is the space of the continuous on Δ, n -dimensional vector-functions with operations in R n; U is σ - algebra in C, created by all possible opened (in C metric) sets; ∠ (R n) is the space of linear operators in R n. The functions shift a(t, x t , u t ) = a u (t, x) and diffusion σ (t, x t ) satisfy the following conditions of smoothness: for example, C1 (Δ0, R1) and C (R n, R n) are the space of continuous differential functions, and the continuous and twice differential functions accordingly. Control (u t )is formed as a function of time and macro variables (x̄ t ), which are nonrandom with respect to set Ω”, and are measured by some physical instruments.
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Lerner, V.S. (2000). Mathematical Foundations of Informational Macrodynamics. In: Information Systems Analysis and Modeling. The Springer International Series in Engineering and Computer Science, vol 532. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4639-9_1
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DOI: https://doi.org/10.1007/978-1-4615-4639-9_1
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