The Wiener–Hopf Equation with Probability Kernel and Submultiplicative Asymptotics of the Inhomogeneous Term
We consider the inhomogeneous Wiener–Hopf equation whose kernel is a nonarithmetic probability distribution with positive mean. The inhomogeneous term behaves like a submultiplicative function. We establish asymptotic properties of the solution to which the successive approximations converge. These...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-09-01
|
| Series: | AppliedMath |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2673-9909/2/3/29 |
| _version_ | 1797466054871482368 |
|---|---|
| author | Mikhail Sgibnev |
| author_facet | Mikhail Sgibnev |
| author_sort | Mikhail Sgibnev |
| collection | DOAJ |
| description | We consider the inhomogeneous Wiener–Hopf equation whose kernel is a nonarithmetic probability distribution with positive mean. The inhomogeneous term behaves like a submultiplicative function. We establish asymptotic properties of the solution to which the successive approximations converge. These properties depend on the asymptotics of the submultiplicative function. |
| first_indexed | 2024-03-09T18:30:34Z |
| format | Article |
| id | doaj.art-abd196374c7f424c9b68373c1119fb29 |
| institution | Directory Open Access Journal |
| issn | 2673-9909 |
| language | English |
| last_indexed | 2024-03-09T18:30:34Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | AppliedMath |
| spelling | doaj.art-abd196374c7f424c9b68373c1119fb292023-11-24T07:33:11ZengMDPI AGAppliedMath2673-99092022-09-012350151110.3390/appliedmath2030029The Wiener–Hopf Equation with Probability Kernel and Submultiplicative Asymptotics of the Inhomogeneous TermMikhail Sgibnev0Sobolev Institute of Mathematics, 630090 Novosibirsk, RussiaWe consider the inhomogeneous Wiener–Hopf equation whose kernel is a nonarithmetic probability distribution with positive mean. The inhomogeneous term behaves like a submultiplicative function. We establish asymptotic properties of the solution to which the successive approximations converge. These properties depend on the asymptotics of the submultiplicative function.https://www.mdpi.com/2673-9909/2/3/29Wiener–Hopf equationinhomogeneous equationnonarithmetic probability distributionpositive meansubmultiplicative functionasymptotic behavior |
| spellingShingle | Mikhail Sgibnev The Wiener–Hopf Equation with Probability Kernel and Submultiplicative Asymptotics of the Inhomogeneous Term AppliedMath Wiener–Hopf equation inhomogeneous equation nonarithmetic probability distribution positive mean submultiplicative function asymptotic behavior |
| title | The Wiener–Hopf Equation with Probability Kernel and Submultiplicative Asymptotics of the Inhomogeneous Term |
| title_full | The Wiener–Hopf Equation with Probability Kernel and Submultiplicative Asymptotics of the Inhomogeneous Term |
| title_fullStr | The Wiener–Hopf Equation with Probability Kernel and Submultiplicative Asymptotics of the Inhomogeneous Term |
| title_full_unstemmed | The Wiener–Hopf Equation with Probability Kernel and Submultiplicative Asymptotics of the Inhomogeneous Term |
| title_short | The Wiener–Hopf Equation with Probability Kernel and Submultiplicative Asymptotics of the Inhomogeneous Term |
| title_sort | wiener hopf equation with probability kernel and submultiplicative asymptotics of the inhomogeneous term |
| topic | Wiener–Hopf equation inhomogeneous equation nonarithmetic probability distribution positive mean submultiplicative function asymptotic behavior |
| url | https://www.mdpi.com/2673-9909/2/3/29 |
| work_keys_str_mv | AT mikhailsgibnev thewienerhopfequationwithprobabilitykernelandsubmultiplicativeasymptoticsoftheinhomogeneousterm AT mikhailsgibnev wienerhopfequationwithprobabilitykernelandsubmultiplicativeasymptoticsoftheinhomogeneousterm |