Counterexamples to mean square almost periodicity of the solutions of some SDEs with almost periodic coefficients
We show that, contrarily to what is claimed in some papers, the nontrivial solutions of some stochastic differential equations with almost periodic coefficients are never mean square almost periodic (but they can be almost periodic in distribution).
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| Language: | English |
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Texas State University
2013-04-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2013/91/abstr.html |
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doaj-b3cdfbc35cef4361944f3b1be7fe8c8b2020-11-25T00:20:41ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912013-04-01201391,17Counterexamples to mean square almost periodicity of the solutions of some SDEs with almost periodic coefficientsOmar MellahPaul Raynaud de FitteWe show that, contrarily to what is claimed in some papers, the nontrivial solutions of some stochastic differential equations with almost periodic coefficients are never mean square almost periodic (but they can be almost periodic in distribution). http://ejde.math.txstate.edu/Volumes/2013/91/abstr.htmlSquare-mean almost periodicalmost periodic in distributionOrnstein-Uhlenbecksemilinear stochastic differential equationstochastic evolution equation |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Omar Mellah Paul Raynaud de Fitte |
| spellingShingle |
Omar Mellah Paul Raynaud de Fitte Counterexamples to mean square almost periodicity of the solutions of some SDEs with almost periodic coefficients Electronic Journal of Differential Equations Square-mean almost periodic almost periodic in distribution Ornstein-Uhlenbeck semilinear stochastic differential equation stochastic evolution equation |
| author_facet |
Omar Mellah Paul Raynaud de Fitte |
| author_sort |
Omar Mellah |
| title |
Counterexamples to mean square almost periodicity of the solutions of some SDEs with almost periodic coefficients |
| title_short |
Counterexamples to mean square almost periodicity of the solutions of some SDEs with almost periodic coefficients |
| title_full |
Counterexamples to mean square almost periodicity of the solutions of some SDEs with almost periodic coefficients |
| title_fullStr |
Counterexamples to mean square almost periodicity of the solutions of some SDEs with almost periodic coefficients |
| title_full_unstemmed |
Counterexamples to mean square almost periodicity of the solutions of some SDEs with almost periodic coefficients |
| title_sort |
counterexamples to mean square almost periodicity of the solutions of some sdes with almost periodic coefficients |
| publisher |
Texas State University |
| series |
Electronic Journal of Differential Equations |
| issn |
1072-6691 |
| publishDate |
2013-04-01 |
| description |
We show that, contrarily to what is claimed in some papers, the nontrivial solutions of some stochastic differential equations with almost periodic coefficients are never mean square almost periodic (but they can be almost periodic in distribution). |
| topic |
Square-mean almost periodic almost periodic in distribution Ornstein-Uhlenbeck semilinear stochastic differential equation stochastic evolution equation |
| url |
http://ejde.math.txstate.edu/Volumes/2013/91/abstr.html |
| work_keys_str_mv |
AT omarmellah counterexamplestomeansquarealmostperiodicityofthesolutionsofsomesdeswithalmostperiodiccoefficients AT paulraynauddefitte counterexamplestomeansquarealmostperiodicityofthesolutionsofsomesdeswithalmostperiodiccoefficients |
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