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1

Stochastic differential inclusions

100%
Kisielewicz M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1997
|
tom 17
|
nr 1-2
51-65
EN
The definition and some existence theorems for stochastic differential inclusions depending only on selections theorems are given.
2

Viability theorems for stochastic inclusions

100%
Kisielewicz M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1995
|
tom 15
|
nr 1
61-42
EN
Sufficient conditions for the existence of solutions to stochastic inclusions $x_t - x_s ∈ ∫^t_s F_τ(x_τ)dτ + ∫^t_s G_τ(x_τ)dw_τ + ∫^t_s∫_{IRⁿ} H_{τ,z}(x_τ)ν̃ (dτ,dz)$ beloning to a given set K of n-dimensional cádlág processes are given.
3
Content available remote

Strong and weak solutions to stochastic inclusions

100%
Kisielewicz M.
Banach Center Publications
|
1995
|
tom 32
|
nr 1
277-286
EN
Existence of strong and weak solutions to stochastic inclusions $x_{t} - x_{s} ∈ ∫^{t}_{s} F_{τ}(x_{τ})dτ + ∫^{t}_{s} G_{τ}(x_{τ})dw_{τ} + ∫^{t}_{s} ∫_{ℝ^{n}} H_{τ,z}(x_{τ})q(dτ,dz)$ and $x_{t} - x_{s} ∈ ∫^{t}_{s} F_{τ}(x_{τ})dτ + ∫^{t}_{s}G_{τ}(x_{τ})dw_{τ} + ∫^{t}_{s}∫_{|z|≤1} H_{τ,z}(x_{τ})q(dτ,dz) + ∫^{t}_{s}∫_{|z|>1} H_{τ,z}(x_{τ})p(dτ,dz)$, where p and q are certain random measures, is considered.
4
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Continuous selection theorems

100%
Kisielewicz M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2005
|
tom 25
|
nr 1
159-163
EN
Continuous approximation selection theorems are given. Hence, in some special cases continuous versions of Fillipov's selection theorem follow.
5
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Controllability theorem for nonlinear dynamical systems

100%
Kisielewicz M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2002
|
tom 22
|
nr 2
225-232
EN
Some sufficient conditions for controllability of nonlinear systems described by differential equation ẋ = f(t,x(t),u(t)) are given.
6
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Properties of generalized set-valued stochastic integrals

100%
Kisielewicz M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2014
|
tom 34
|
nr 1
131-147
EN
The paper is devoted to properties of generalized set-valued stochastic integrals defined in [10]. These integrals generalize set-valued stochastic integrals defined by E.J. Jung and J.H. Kim in the paper [4]. Up to now we were not able to construct any example of set-valued stochastic processes, different on a singleton, having integrably bounded set-valued integrals defined in [4]. It was shown by M. Michta (see [11]) that in the general case set-valued stochastic integrals defined by E.J. Jung and J.H. Kim, are not integrably bounded. Generalized set-valued stochastic integrals, considered in the paper, are in some non-trivial cases square integrably bounded and can be applied in the theory of stochastic differential equations with set-valued solutions.
7
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Boundedness of set-valued stochastic integrals

100%
Kisielewicz M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2015
|
tom 35
|
nr 2
197-207
EN
The paper deals with integrably boundedness of Itô set-valued stochastic integrals defined by E.J. Jung and J.H. Kim in the paper [4], where has not been proved that this integral is integrably bounded. The problem of integrably boundedness of the above set-valued stochastic integrals has been considered in the paper [7] and the monograph [8], but the problem has not been solved there. The first positive results dealing with this problem due to M. Michta, who showed (see [11]) that there are bounded set-valued 𝔽-nonanticipative mappings having unbounded Itô set-valued stochastic integrals defined by E.J. Jung and J.H. Kim. The present paper contains some new conditions implying unboundedness of the above type set-valued stochastic integrals.
8
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Tightness of Continuous Stochastic Processes

100%
Kisielewicz M.
Discussiones Mathematicae Probability and Statistics
|
2006
|
tom 26
|
nr 2
151-162
EN
Some sufficient conditins for tightness of continuous stochastic processes is given. It is verified that in the classical tightness sufficient conditions for continuous stochastic processes it is possible to take a continuous nondecreasing stochastic process instead of a deterministic function one.
9
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Selection theorems for stochastic set-valued integrals

100%
Kisielewicz M.
Discussiones Mathematicae Probability and Statistics
|
2001
|
tom 21
|
nr 1
63-75
EN
Some special selections theorems for stochastic set-valued integrals with respect to the Lebesgue measure are given.
10
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Some properties of set-valued stochastic integrals of multiprocesses with finite Castaing representations

100%
Kisielewicz M.
Commentationes Mathematicae
|
2013
|
tom 53
|
nr 2
EN
The paper contains new properties of set-valued stochastic integrals defined as multifunctions with subtrajectory integrals equal to closed decomposable hulls of functional set-valued integrals defined in the author paper [8]. In particular, it is proved that such defined integrals for set-valued predictable square integrably bounded processes having finite Castaing representations are square integrably bounded. Up to now this property has not been proved. Unfortunately, in the general case the above boundedness problem is still open.
11

Some remarks on boundary value problem for differential inclusions

100%
Kisielewicz M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1997
|
tom 17
|
nr 1-2
43-49
EN
Some sufficient conditions for the existence of solutions to boundary value problem for differential inclusions are given.
12

Stochastic differential inclusions

100%
Kisielewicz M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1999
|
tom 19
|
nr 1-2
123-129
EN
The definition and some existence theorems for stochastic differential inclusion dZₜ ∈ F(Zₜ)dXₜ, where F and X are set valued stochastic processes, are given.
13
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On the nonconvergence of successive approximations in the theory of the equation $z"_{xy} = f(x, y, z, z'_x,z'_y)$

88%
Kisielewicz M.
Annales Polonici Mathematici
|
1979
|
tom 36
|
nr 1
85-93
14
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Existence, uniqueness and continuous dependence of solutions of differential equations in Banach space

75%
Kisielewicz M.
Annales Polonici Mathematici
|
1989-1990
|
tom 50
|
nr 2
117-128
15
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Description of a class of multivalued differential equations with almost weakly stable trivial solution

75%
Kisielewicz M.
Annales Polonici Mathematici
|
1980
|
tom 38
|
nr 2
201-205
16
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The Orlicz type theorem for differential-integral equations with a lagging argument

63%
Kisielewicz M.
Annales Polonici Mathematici
|
1975-1976
|
tom 31
|
nr 1
65-71
17
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Generalized functional-differential equations of neutral type

50%
Kisielewicz M.
Annales Polonici Mathematici
|
1983
|
tom 42
|
nr 1
139-148
18
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On some applications of Bogoliubov method for hyperbolic equations

50%
Kisielewicz M.
Annales Polonici Mathematici
|
1975-1976
|
tom 31
|
nr 1
1-13
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