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On approximations of nonzero-sum uniformly continuous ergodic stochastic games

Andrzej Nowak (1999)

Applicationes Mathematicae

We consider a class of uniformly ergodic nonzero-sum stochastic games with the expected average payoff criterion, a separable metric state space and compact metric action spaces. We assume that the payoff and transition probability functions are uniformly continuous. Our aim is to prove the existence of stationary ε-equilibria for that class of ergodic stochastic games. This theorem extends to a much wider class of stochastic games a result proven recently by Bielecki [2].

On exact null controllability of Black-Scholes equation

Kumarasamy Sakthivel, Krishnan Balachandran, Rangarajan Sowrirajan, Jeong-Hoon Kim (2008)

Kybernetika

In this paper we discuss the exact null controllability of linear as well as nonlinear Black–Scholes equation when both the stock volatility and risk-free interest rate influence the stock price but they are not known with certainty while the control is distributed over a subdomain. The proof of the linear problem relies on a Carleman estimate and observability inequality for its own dual problem and that of the nonlinear one relies on the infinite dimensional Kakutani fixed point theorem with L 2 ...

On infinite horizon active fault diagnosis for a class of non-linear non-Gaussian systems

Ivo Punčochář, Miroslav Šimandl (2014)

International Journal of Applied Mathematics and Computer Science

The paper considers the problem of active fault diagnosis for discrete-time stochastic systems over an infinite time horizon. It is assumed that the switching between a fault-free and finitely many faulty conditions can be modelled by a finite-state Markov chain and the continuous dynamics of the observed system can be described for the fault-free and each faulty condition by non-linear non-Gaussian models with a fully observed continuous state. The design of an optimal active fault detector that...

On solutions set of a multivalued stochastic differential equation

Marek T. Malinowski, Ravi P. Agarwal (2017)

Czechoslovak Mathematical Journal

We analyse multivalued stochastic differential equations driven by semimartingales. Such equations are understood as the corresponding multivalued stochastic integral equations. Under suitable conditions, it is shown that the considered multivalued stochastic differential equation admits at least one solution. Then we prove that the set of all solutions is closed and bounded.

Optimal erasures in decision-feedback equalization for the Gaussian noise

Jerzy Kisilewicz, Arkadiusz Grzybowski (2006)

International Journal of Applied Mathematics and Computer Science

A new method of optimizing decision feedback parameters for intersymbol interference equalizers is described. The coefficient existing in the decision feedback loop depends on risk qualification of the received decision. We prove that bit error probability can be decreased with this method for any channel with a single interference sample and small Gaussian noise. Experimental results are presented for selected channels. The dependences of optimal feedback parameters on channel interference samples...

Optimal solutions to stochastic differential inclusions

Mariusz Michta (2002)

Applicationes Mathematicae

A martingale problem approach is used first to analyze compactness and continuous dependence of the solution set to stochastic differential inclusions of Ito type with convex integrands on the initial distributions. Next the problem of existence of optimal weak solutions to such inclusions and their dependence on the initial distributions is investigated.

Optimized state estimation for nonlinear dynamical networks subject to fading measurements and stochastic coupling strength: An event-triggered communication mechanism

Chaoqing Jia, Jun Hu, Chongyang Lv, Yujing Shi (2020)

Kybernetika

This paper is concerned with the design of event-based state estimation algorithm for nonlinear complex networks with fading measurements and stochastic coupling strength. The event-based communication protocol is employed to save energy and enhance the network transmission efficiency, where the changeable event-triggered threshold is adopted to adjust the data transmission frequency. The phenomenon of fading measurements is described by a series of random variables obeying certain probability distribution....

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