COUNTEREXAMPLES TO MEAN SQUARE ALMOST PERIODICITY OF THE SOLUTIONS OF SOME SDES WITH ALMOST PERIODIC COEFFICIENTS

By O. Mellah, P. R. D. Fitte. 2012

47 citations recorded by the source corpus.

We show that, contrarily to what is claimed in some papers, the nontrivial solutions of some stochastic differential equations with almost pe- riodic coefficients are never mean square almost periodic (but they can be almost periodic in distribution).

Subfields: Applied Mathematics, Control and Systems Engineering, Finance

View Paper: https://www.semanticscholar.org/paper/18c25ab65c5ef35cb7f3f9595c0733c4afb1ded8

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1. M. Kamenski
2. P. R. D. Fitte
3. O. Mellah

Citations in the corpus

• Weak averaging of semilinear stochastic differential equations with almost periodic coefficients (2012, background): “The second group claims the existence of square mean almost periodic solutions, but square mean almost periodicity seems to be a too strong property for solutions of SDEs, see counterexamples in [14].”