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Stochastic control optimal in the Kullback sense

Jan Šindelář, Igor Vajda, Miroslav Kárný (2008)

Kybernetika

The paper solves the problem of minimization of the Kullback divergence between a partially known and a completely known probability distribution. It considers two probability distributions of a random vector ( u 1 , x 1 , ... , u T , x T ) on a sample space of 2 T dimensions. One of the distributions is known, the other is known only partially. Namely, only the conditional probability distributions of x τ given u 1 , x 1 , ... , u τ - 1 , x τ - 1 , u τ are known for τ = 1 , ... , T . Our objective is to determine the remaining conditional probability distributions of u τ given u 1 , x 1 , ... , u τ - 1 , x τ - 1 such...

Stochastic differential games involving impulse controls

Feng Zhang (2011)

ESAIM: Control, Optimisation and Calculus of Variations

A zero-sum stochastic differential game problem on infinite horizon with continuous and impulse controls is studied. We obtain the existence of the value of the game and characterize it as the unique viscosity solution of the associated system of quasi-variational inequalities. We also obtain a verification theorem which provides an optimal strategy of the game.

Stochastic differential games involving impulse controls*

Feng Zhang (2011)

ESAIM: Control, Optimisation and Calculus of Variations

A zero-sum stochastic differential game problem on infinite horizon with continuous and impulse controls is studied. We obtain the existence of the value of the game and characterize it as the unique viscosity solution of the associated system of quasi-variational inequalities. We also obtain a verification theorem which provides an optimal strategy of the game.

Stochastic invariance and consistency of financial models

Jerzy Zabczyk (2000)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The paper is devoted to a connection between stochastic invariance in infinite dimensions and a consistency question of mathematical finance. We derive necessary and sufficient conditions for stochastic invariance of Nagumo’s type for stochastic equations with additive noise. They are applied to Ornstein-Uhlenbeck processes and to specific financial models. The case of evolution equations with general noise is discussed also and a comparison with recent results obtained by geometric methods is presented...

Stochastic stability in spatial games

Jacek Miękisz (2008)

Banach Center Publications

We compare two concepts of stochastic stability in spatial games. The classical approach to stochastic stability, introduced by Foster and Young [8], involves single configurations in the zero-noise limit. Ensemble stability discussed in [17] refers to ensembles of configurations in the limit of an infinite number of players. The above two limits may not commute. We will discuss reasons of such behaviour. We review some results concerning the effect of the number of players and the noise level on...

Stock price forecasting: Autoregressive modelling and fuzzy neural network.

Dusan Marcek (2000)

Mathware and Soft Computing

Most models for the time series of stock prices have centered on autoregresive (AR) processes. Traditionaly, fundamental Box-Jenkins analysis [3] have been the mainstream methodology used to develop time series models. Next, we briefly describe the develop a classical AR model for stock price forecasting. Then a fuzzy regression model is then introduced. Following this description, an artificial fuzzy neural network based on B-spline member ship function is presented as an alternative to the stock...

Strong functors and interleaving fixpoints in game semantics

Pierre Clairambault (2013)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We describe a sequent calculus μLJ with primitives for inductive and coinductive datatypes and equip it with reduction rules allowing a sound translation of Gödel’s system T. We introduce the notion of a μ-closed category, relying on a uniform interpretation of open μLJ formulas as strong functors. We show that any μ-closed category is a sound model for μLJ. We then turn to the construction of a concrete μ-closed category based on Hyland-Ong game semantics. The model relies on three main ingredients:...

Structural analysis of social networks with respect to different levels of aggregation

Hans J. Hummell, Wolfgang Sodeur (1997)

Mathématiques et Sciences Humaines

The article aims at the integration of the two research traditions of multi-level and of network analysis. To this effect, a strategy is presented which can be traced back to P.F. Lazarsfeld and H. Menzel's typology of units and of their properties. After having extended their classification to take account of more network concepts than was needed at their time, the Lazarsfeld-Menzel-Classification is used as a conceptual instrument to translate a research question, which first looks like a specialty...

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