Evelyn Buckwar, John A.D. Appleby,
"Noise induced oscillation in solutions of stochastic delay differential equations"
, in Dynamic Systems and Applications, Vol. 14, Nummer 2, Dynamic Publishers, Inc., Atlanta, Seite(n) 175-196, 2005, ISSN: 1056-2176
Noise induced oscillation in solutions of stochastic delay differential equations
Sprache des Titels:
This paper studies the oscillatory properties of solutions of linear
scalar stochastic delay di®erential equations with multiplicative noise. It is
shown that such noise will induce an oscillation in the solution whenever there
is negative feedback from the delay term. The zeros of the process are a
countable set; the solution is di®erentiable at each zero, and the zeros are
simple. The addition of such noise does not alter the positivity of solutions
when there is positive feedback.