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Law equivalence of solutions of some linear stochastic equations in Hilbert spaces

100%
Peszat S.
Studia Mathematica
|
1991-1992
|
tom 101
|
nr 3
269-284
EN
Sufficient and necessary conditions for equivalence of the distributions of the solutions of some linear stochastic equations in Hilbert spaces are given. Some facts in the theory of perturbations of semigroup generators and Zabczyk's results on law equivalence are used.
2
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Space-time continuous solutions to SPDE's driven by a homogeneous Wiener process

63%
Brzeźniak Z., Peszat S.
Studia Mathematica
|
1999
|
tom 137
|
nr 3
261-299
EN
Stochastic partial differential equations on $ℝ^d$ are considered. The noise is supposed to be a spatially homogeneous Wiener process. Using the theory of stochastic integration in Banach spaces we show the existence of a Markovian solution in a certain weighted $L^q$-space. Then we obtain the existence of a space continuous solution by means of the Da Prato, Kwapień and Zabczyk factorization identity for stochastic convolutions.
3
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Research problems of Jerzy Zabczyk

63%
Peszat S., Stettner Ł.
Banach Center Publications
|
2015
|
tom 105
|
nr 1
9-32
EN
In the paper we present a selected variety of problems studied by Professor Jerzy Zabczyk. Important part of Prof. Zabczyk's scientific activity was devoted to his PhD students. He has promoted 9 PhD students: Tomasz Bielecki, Jarosław Sobczyk, Łukasz Stettner and Gianmario Tessitore work mostly in control and its applications to mathematical finance, whereas the research of Anna Chojnowska-Michalik, Wojciech Jachimiak, Anna Milian, Szymon Peszat and Anna Rusinek is concentrated mostly on stochastic evolution equations. Description of research problems of Prof. Jerzy Zabczyk starts from infinite-dimensional (deterministic) control problems, stochastic control problems: optimal choice problems, stopping time problems, to come first to mathematics of finance and then to stochastic analysis: stochastic evolution and partial differential equations. We show main results and point out their importance. The paper is based on the presentation of the authors during a special session at the conference.
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