Displaying similar documents to “Asymptotic and exponential decay in mean square for delay geometric Brownian motion”

Hitting distributions of geometric Brownian motion

T. Byczkowski, M. Ryznar (2006)

Studia Mathematica

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Let τ be the first hitting time of the point 1 by the geometric Brownian motion X(t) = x exp(B(t) - 2μt) with drift μ ≥ 0 starting from x > 1. Here B(t) is the Brownian motion starting from 0 with EB²(t) = 2t. We provide an integral formula for the density function of the stopped exponential functional A ( τ ) = ∫ 0 τ X ² ( t ) d t and determine its asymptotic behaviour at infinity. Although we basically rely on methods developed in [BGS], the present paper covers the case of arbitrary drifts μ ≥ 0 and provides...

Non-exponential and polynomial stability results of a Bresse system with one infinite memory in the vertical displacement

Aissa Guesmia (2017)

Nonautonomous Dynamical Systems

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The asymptotic stability of one-dimensional linear Bresse systems under infinite memories was obtained by Guesmia and Kafini [10] (three infinite memories), Guesmia and Kirane [11] (two infinite memories), Guesmia [9] (one infinite memory acting on the longitudinal displacement) and De Lima Santos et al. [6] (one infinite memory acting on the shear angle displacement). When the kernel functions have an exponential decay at infinity, the obtained stability estimates in these papers lead...

Global well-posedness and energy decay for a one dimensional porous-elastic system subject to a neutral delay

Houssem Eddine Khochemane, Sara Labidi, Sami Loucif, Abdelhak Djebabla (2025)

Mathematica Bohemica

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We consider a one-dimensional porous-elastic system with porous-viscosity and a distributed delay of neutral type. First, we prove the global existence and uniqueness of the solution by using the Faedo-Galerkin approximations along with some energy estimates. Then, based on the energy method with some appropriate assumptions on the kernel of neutral delay term, we construct a suitable Lyapunov functional and we prove that, despite of the destructive nature of delays in general, the damping...

On exponential stability of second order delay differential equations

Ravi P. Agarwal, Alexander Domoshnitsky, Abraham Maghakyan (2015)

Czechoslovak Mathematical Journal

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We propose a new method for studying stability of second order delay differential equations. Results we obtained are of the form: the exponential stability of ordinary differential equation implies the exponential stability of the corresponding delay differential equation if the delays are small enough. We estimate this smallness through the coefficients of this delay equation. Examples demonstrate that our tests of the exponential stability are essentially better than the known ones....

On the dynamics of equations with infinite delay

Dalibor Pražák (2006)

Open Mathematics

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We consider a system of ordinary differential equations with infinite delay. We study large time dynamics in the phase space of functions with an exponentially decaying weight. The existence of an exponential attractor is proved under the abstract assumption that the right-hand side is Lipschitz continuous. The dimension of the attractor is explicitly estimated.