[Turkmath:7020] AIBU: Viorica Ungureanu Seminerleri

[cenap ozel]

Degerli Liste Uyeleri,

Romanya Constantin Brancusi Universitesinden Viorica Ungureanu
Abant Izzet Baysal Universitesi Matematik Bolumunu 10-11 Mayis tarihlerinde
Erasmus kapsaminda ziyaret edecektir.

Profesor Ungureanu bu donemde asagida detaylari verilmis konusmalari
verecektir.

İlgilerinize saygilarimla arz ederim.


Cenap Ozel


"*Stochastic Differential Equations* "

In this talk we present a set of prerequisites concerning linear
stochastic differential

equations (LSDE for short) with multiplicative noise in Hilbert spaces.

First, we brie.y recall basic facts concerning stochastic integral,

Ito.s formula and existence and approximation problems for the
LSDEs.solutions. Two representation results,

involving the covariance operators associated with the solutions of
LSDEs, are then discussed.

One of them essentially states that the covariance operator is the
unique solution of an initial

value problem described by a linear di¤erential equation defined on a space of

nuclear operators. The other establishes a connection between the
nuclear norm of the

covariance operator and the solution of certain backward Lyapunov equation.

Finally, we discuss stability problems for LSDEs.solutions by using
two approaches.

The first one is classical (see e.g [1]) and provides necessary and
sufcient conditions for

the uniform exponential stability of Datko type, or equivalently, of
Lyapunov type.

The second ([2], [3]) is new and based on the new representation
results mentioned above.

This approach is useful not only in solving stability problems for
LSDEs but also in treating many

other problems which need a computation of the mean square of the solutions.

[1] G. Da.Prato, A. Ichikawa, Lyapunov equations for time-varying
linear systems ,

Systems and Control Letters 9(1987), pp. 165-172.

[2] V. M. Ungureanu, Stochastic uniform observability of linear
differential equations with

multiplicative noise,J. Math. Anal. Appl. 343 (2008), no. 1, 446.463.

[3] V. M. Ungureanu, Representations of mild solutions of time-varying
linear stochastic

equations and the exponential stability of periodic systems,

Electronic Journal of Qualitative Theory of Differential equations,
nr. 4, 2004, pp. 1-22.

Viorica Ungureanu,
Constantin Brancusi University, Romania

Tarih: 10 Mayıs 2010 Pazartesi

* Saat: *15.30

Yer: 138 no.lu Seminer Salonu





*"** Optimal control of linear stochastic evolution
equations in Hilbert spaces and uniform observability* "

This talk concerns a linear quadratic (LQ) problem associated with linear
stochastic evolution equations(LSEE) with unbounded coe¢ cients in the
drift. It is well known that the existence of some global nonnegative
solutions of the di¤erential Riccati equations (DRE), arrisen in connection
with LSEE, plays an important role in solving LQ problems. Since stochastic
observability property is closely related to this subject, we begin by
giving a deterministic characterization of this notion. Then we show that,
under stabilizability and stochastic uniform observability or detectability
conditions, the Riccati equations of stochastic control have nonnegative,
bounded on R+ and stabilizing solutions [1]. Based on this result, the LQ
problems can be solved [1].

[1] V. M. Ungureanu, Optimal control of linear stochastic evolution
equations in Hilbert spaces and uniform observability, to appear in
Czechoslovak
Mathematical Journal.

Viorica Ungureanu,

Constantin Brancusi University, Romania



Tarih: 11 Mayıs 2010 Salı

* *Saat: 15.30

Yer: 138 no.lu Seminer Salonu
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