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.

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...

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....

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...

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...

Under the key assumption of finite $\rho$-variation, $\rho \in [1,2)$, 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), $\rho =1$ resp. $\rho =1/\left(2H\right)$, 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 $k^{-(1/\rho -1/2-\epsilon )}$, any $\epsilon gt;0$, for Wong–Zakai and Milstein-type...

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 $\phi$ satisfying $X_{s+t}=\phi (X_s,t,P_s,u_s)$ and $\mathrm{d}{X}_t=\mathrm{E}[u_0\left(X_0\right)/X_t]\mathrm{d}t$, where $P_s=P{X}_s^{-1}$ is the law of $X_s$ and $u_s\left(x\right)=\mathrm{E}[u_0\left(X_0\right)/X_s=x]$ is the velocity of particle $x$ at time $s\ge 0$. Results on the flow characterization and Lipschitz continuity are also given.Moreover, the map $(x,t)\mapsto M(x,t):=P(X_t\le x)$ is the entropy solution of a scalar conservation law ${\partial }_{t}M+{\partial }_x\left(A\left(M\right)\right)=0$ where the flux $A$ represents the particles...