Differentiable selections of multifunctions and their applications

Michta, Mariusz; Motyl, Jerzy

doi:10.1016/j.na.2005.12.001

Cited by 10 publications

(6 citation statements)

References 7 publications

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“…In this section we recall the notion of set-valued Stratonovich stochastic integral and some existence results connected with the Stratonovich stochastic inclusion described in [1]. Let (Ω, F , (F t ) t∈[0,T ] , P) denote a complete filtered probability space satisfying the usual conditions.…”

Section: Set-valued Stratonovich Integral and Stochastic Inclusionmentioning

confidence: 99%

“…The notions of set-valued Stratonovich stochastic integrals and Stratonovich stochastic inclusions have been introduced recently by the authors in [1,2]. In [1] the existence of continuously differentiable selections for set-valued functions has been studied in order to establish the existence of weak solutions to such inclusions.…”

Section: Introductionmentioning

confidence: 99%

“…In [1] the existence of continuously differentiable selections for set-valued functions has been studied in order to establish the existence of weak solutions to such inclusions. In the present paper we continue the study on the subject.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Martingale problem to Stratonovich stochastic inclusion

Michta

Motyl

2009

Nonlinear Analysis: Theory, Methods & Applications

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Section: Set-valued Stratonovich Integral and Stochastic Inclusionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Martingale problem to Stratonovich stochastic inclusion

Michta

Motyl

2009

Nonlinear Analysis: Theory, Methods & Applications

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“…[1,4,13,22,26,37]. Later, the notion of the integral for set-valued functions has been extended to a stochastic case where set-valued Itô and Stratonovich integrals have been studied and applied to stochastic differential inclusions and set-valued stochastic differential equations, see e.g., [23][24][25][33][34][35]. Moreover, concepts of set-valued integrals, both deterministic and stochastic, were used to define the notion of fuzzy integrals applied in the theory of fuzzy differential equations, e.g., [16,21,27,32].…”

Section: Introductionmentioning

confidence: 99%

Selection Properties and Set-Valued Young Integrals of Set-Valued Functions

Michta

Motyl

2020

Results Math

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The paper deals with some selection properties of set-valued functions and different types of set-valued integrals of a Young type. Such integrals are considered for classes of Hölder continuous or with bounded Young p-variation set-valued functions. Two different cases are considered, namely set-valued functions with convex values and without convexity assumptions. The integrals contain as a particular case set-valued stochastic integrals with respect to a fractional Brownian motion, and therefore, their properties are crucial for the investigation of solutions to stochastic differential inclusions driven by a fractional Brownian motion.

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“…On the other hand, although there exists a wide literature where attempts have been made to investigate stochastic differential inclusions (see e.g. [20][21][22][23][24]32] and references therein), it seems, as far as we know, that the problem of the existence and properties of solutions to stochastic set differential equations is still open. In this paper we present the existence and uniqueness of solutions for such stochastic equations as well as other typical properties.…”

Section: Introductionmentioning

confidence: 99%