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Controllability of semilinear stochastic integrodifferential systems

Krishnan Balachandran, S. Karthikeyan, Jeong-Hoon Kim (2007)

Kybernetika

In this paper we study the approximate and complete controllability of stochastic integrodifferential system in finite dimensional spaces. Sufficient conditions are established for each of these types of controllability. The results are obtained by using the Picard iteration technique.

Controllability of three-dimensional Navier–Stokes equations and applications

Armen Shirikyan (2005/2006)

Séminaire Équations aux dérivées partielles

We formulate two results on controllability properties of the 3D Navier–Stokes (NS) system. They concern the approximate controllability and exact controllability in finite-dimensional projections of the problem in question. As a consequence, we obtain the existence of a strong solution of the Cauchy problem for the 3D NS system with an arbitrary initial function and a large class of right-hand sides. We also discuss some qualitative properties of admissible weak solutions for randomly forced NS...

Controlling the stochastic sensitivity in thermochemical systems under incomplete information

Irina Bashkirtseva (2018)

Kybernetika

Complex dynamic regimes connected with the noise-induced mixed-mode oscillations in the thermochemical model of flow reactor are studied. It is revealed that the underlying reason of such excitability is in the high stochastic sensitivity of the equilibrium. The problem of stabilization of the excitable equilibrium regimes is investigated. We develop the control approach using feedback regulators which reduce the stochastic sensitivity and keep the randomly forced system near the stable equilibrium....

Convergence analysis for asymmetric Deffuant-Weisbuch model

Jiangbo Zhang (2014)

Kybernetika

In this paper, we investigate the convergence behavior of the asymmetric Deffuant-Weisbuch (DW) models during the opinion evolution. Based on the convergence of the asymmetric DW model that generalizes the conventional DW model, we first propose a new concept, the separation time, to study the transient behavior during the DW model's opinion evolution. Then we provide an upper bound of the expected separation time with the help of stochastic analysis. Finally, we show relations of the separation...

Convergence model of interest rates of CKLS type

Zuzana Zíková, Beáta Stehlíková (2012)

Kybernetika

This paper deals with convergence model of interest rates, which explains the evolution of interest rate in connection with the adoption of Euro currency. Its dynamics is described by two stochastic differential equations – the domestic and the European short rate. Bond prices are then solutions to partial differential equations. For the special case with constant volatilities closed form solutions for bond prices are known. Substituting its constant volatilities by instantaneous volatilities we...

Convergence rates for the full gaussian rough paths

Peter Friz, Sebastian Riedel (2014)

Annales de l'I.H.P. Probabilités et statistiques

Under the key assumption of finite ρ -variation, ρ [ 1 , 2 ) , of the covariance of the underlying Gaussian process, sharp a.s. convergence rates for approximations of Gaussian rough paths are established. When applied to Brownian resp. fractional Brownian motion (fBM), ρ = 1 resp. ρ = 1 / ( 2 H ) , we recover and extend the respective results of (Trans. Amer. Math. Soc.361 (2009) 2689–2718) and (Ann. Inst. Henri Poincasé Probab. Stat.48(2012) 518–550). In particular, we establish an a.s. rate k - ( 1 / ρ - 1 / 2 - ε ) , any ε g t ; 0 , for Wong–Zakai and Milstein-type...

Convex hulls, Sticky particle dynamics and Pressure-less gas system

Octave Moutsinga (2008)

Annales mathématiques Blaise Pascal

We introduce a new condition which extends the definition of sticky particle dynamics to the case of discontinuous initial velocities u 0 with negative jumps. We show the existence of a stochastic process and a forward flow φ satisfying X s + t = φ ( X s , t , P s , u s ) and d X t = E [ u 0 ( X 0 ) / X t ] d t , where P s = P X s - 1 is the law of X s and u s ( x ) = E [ u 0 ( X 0 ) / X s = x ] is the velocity of particle x at time s 0 . Results on the flow characterization and Lipschitz continuity are also given.Moreover, the map ( x , t ) M ( x , t ) : = P ( X t x ) is the entropy solution of a scalar conservation law t M + x ( A ( M ) ) = 0 where the flux A represents the particles...

Currently displaying 341 – 360 of 1721