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Equazione stocastica di dinamica di popolazioni di tipo preda-predatore

Sonia Chessa, Hisao Fujita Yashima (2002)

Bollettino dell'Unione Matematica Italiana

Si considera l'equazione stocastica che modellizza la dinamica di popolazioni di due specie di tipo preda-predatore sotto perturbazioni stocastiche. Si dimostrano in primo luogo l'esistenza e l'unicità della soluzione dell'equazione; per questo è essenziale introdurre una funzione ausiliaria con cui si costruiscono soluzioni approssimate. Si dimostra inoltre che, se non sono presenti perturbazioni stocastiche dovute alla stocasticità demografica, ma solo perturbazioni stocastiche rappresentanti...

Equivalent cost functionals and stochastic linear quadratic optimal control problems

Zhiyong Yu (2013)

ESAIM: Control, Optimisation and Calculus of Variations

This paper is concerned with the stochastic linear quadratic optimal control problems (LQ problems, for short) for which the coefficients are allowed to be random and the cost functionals are allowed to have negative weights on the square of control variables. We propose a new method, the equivalent cost functional method, to deal with the LQ problems. Comparing to the classical methods, the new method is simple, flexible and non-abstract. The new method can also be applied to deal with nonlinear...

Ergodic behaviour of stochastic parabolic equations

Jan Seidler (1997)

Czechoslovak Mathematical Journal

The ergodic behaviour of homogeneous strong Feller irreducible Markov processes in Banach spaces is studied; in particular, existence and uniqueness of finite and σ -finite invariant measures are considered. The results obtained are applied to solutions of stochastic parabolic equations.

Ergodicity for a stochastic geodesic equation in the tangent bundle of the 2D sphere

Ľubomír Baňas, Zdzisław Brzeźniak, Mikhail Neklyudov, Martin Ondreját, Andreas Prohl (2015)

Czechoslovak Mathematical Journal

We study ergodic properties of stochastic geometric wave equations on a particular model with the target being the 2D sphere while considering only solutions which are independent of the space variable. This simplification leads to a degenerate stochastic equation in the tangent bundle of the 2D sphere. Studying this equation, we prove existence and non-uniqueness of invariant probability measures for the original problem and obtain also results on attractivity towards an invariant measure. We also...

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