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On a stochastic SIR model

Elisabetta Tornatore, Stefania Maria Buccellato (2007)

Applicationes Mathematicae

We consider a stochastic SIR system and we prove the existence, uniqueness and positivity of solution. Moreover the existence of an invariant measure under a suitable condition on the coefficients is studied.

On small solutions of second order differential equations with random coefficients

László Hatvani, László Stachó (1998)

Archivum Mathematicum

We consider the equation x ' ' + a 2 ( t ) x = 0 , a ( t ) : = a k if t k - 1 t < t k , for k = 1 , 2 , ... , where { a k } is a given increasing sequence of positive numbers, and { t k } is chosen at random so that { t k - t k - 1 } are totally independent random variables uniformly distributed on interval [ 0 , 1 ] . We determine the probability of the event that all solutions of the equation tend to zero as t .

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