A Probabilistic Approximation of the Cauchy Problem Solution for the Schrödinger Equation with a Fractional Derivative Operator
| Autor: | M. V. Platonova, S. V. Tsykin |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Applied Mathematics General Mathematics Operator (physics) 010102 general mathematics Probabilistic logic Expected value 01 natural sciences 010305 fluids & plasmas Schrödinger equation Fractional calculus symbols.namesake Distribution (mathematics) 0103 physical sciences symbols Applied mathematics Initial value problem 0101 mathematics Random variable Mathematics |
| Zdroj: | Journal of Mathematical Sciences. 244:874-884 |
| ISSN: | 1573-8795 1072-3374 |
| DOI: | 10.1007/s10958-020-04659-7 |
| Popis: | We construct two types of probabilistic approximations of the Cauchy problem solution for the nonstationary Schrodinger equation with a symmetric fractional derivative of order α ∈ (1, 2) at the right-hand side. In the first case, we approximate the solution by mathematical expectation of point Poisson field functionals, and in the second case, we approximate the solution by mathematical expectation of functionals of sums of independent random variables having a power asymptotics of a tail distribution. |
| Databáze: | OpenAIRE |
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