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On \(\mathbb{I}\)-approximate limits and \(\mathbb{I}\)-approximate smoothness

100%

Zduńczyk R.

Commentationes Mathematicae

2006

tom 46

nr 1

In this paper we present some results based on slightly modified idea of the \(\mathbb{I}\)-density introduced by Władysław Wilczyński. Some theorems are generalized versions of results from [2] and [3]. We investigate properties of functions from \(\mathbb{R}^X\), where \(X\) is supplied with the \(\mathbb{I}\)-density. We try to free our considerations from the assumption of Baire property, or measurability. In some cases this is not done yet. Star-marked statements still need that assumption, proofs presented here are done for Baire property, but it is possible to adapt them to measure. \(\mathbb{I}\)-density itself does not require any structure of considered space but a metric vector space over \(\mathbb{R}\). However, in last section we confine ourselves to \(\mathbb{R}\), for we make use of \(\mathbb{R}\)’s structure for simplicity. To find more about related topics see [4], [5], more bibliography one can find in [1] and [5].

A multidimensional singular stochastic control problem on a finite time horizon

100%

Boryc M., Kruk Ł.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2015

tom 69

nr 1

A singular stochastic control problem in n dimensions with timedependent coefficients on a finite time horizon is considered. We show that the value function for this problem is a generalized solution of the corresponding HJB equation with locally bounded second derivatives with respect to the space variables and the first derivative with respect to time. Moreover, we prove that an optimal control exists and is unique.

Ograniczanie wyników

1 Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

1 Commentationes Mathematicae

1 Boryc M.

1 Kruk Ł.

1 Zduńczyk R.

1 2015

1 2006

Wyniki wyszukiwania

On \(\mathbb{I}\)-approximate limits and \(\mathbb{I}\)-approximate smoothness

A multidimensional singular stochastic control problem on a finite time horizon