scholarly journals Mean reversion for HJMM forward rate models

2010 ◽  
Vol 42 (2) ◽  
pp. 371-391 ◽  
Author(s):  
Anna Rusinek
Keyword(s):  
State Space ◽  
Mean Reversion ◽  
The State ◽  
Forward Rate ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Forward Rates ◽  
Infinite Dimensional ◽  
Long Time ◽  
Special Case

We examine the long-time behavior of forward rates in the framework of Heath-Jarrow-Morton-Musiela models with infinite-dimensional Lévy noise. We give an explicit condition under which the rates have a mean reversion property. In a special case we show that this condition is fulfilled for any Lévy process with variance smaller than a given constant, depending only on the state space and the volatility.

scholarly journals Mean reversion for HJMM forward rate models

2010 ◽  
Vol 42 (02) ◽  
pp. 371-391 ◽  
Author(s):  
Anna Rusinek
Keyword(s):  
State Space ◽  
Mean Reversion ◽  
The State ◽  
Forward Rate ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Forward Rates ◽  
Infinite Dimensional ◽  
Long Time ◽  
Special Case

We examine the long-time behavior of forward rates in the framework of Heath-Jarrow-Morton-Musiela models with infinite-dimensional Lévy noise. We give an explicit condition under which the rates have a mean reversion property. In a special case we show that this condition is fulfilled for any Lévy process with variance smaller than a given constant, depending only on the state space and the volatility.

scholarly journals Attractors for Multivalued Impulsive Systems: Existence and Applications to Reaction-Diffusion System

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
S. Dashkovskiy ◽  
O. A. Kapustian ◽  
O. V. Kapustyan ◽  
N. V. Gorban
Keyword(s):  
Initial Conditions ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Impulsive Systems ◽  
Uniform Attractor ◽  
Infinite Dimensional ◽  
Long Time

In this paper, we develop a general approach to investigate limit dynamics of infinite-dimensional dissipative impulsive systems whose initial conditions do not uniquely determine their long time behavior. Based on the notion of an uniform attractor, we show how to describe limit behavior of such complex systems with the help of properties of their components. More precisely, we prove the existence of the uniform attractor for an impulsive multivalued system in terms of properties of nonimpulsive semiflow and impulsive parameters. We also give an application of these abstract results to the impulsive reaction-diffusion system without uniqueness.

scholarly journals The well-posedness and long-time behavior of the nonlocal diffusion porous medium equations with nonlinear term

2021 ◽  
Author(s):  
Chang Zhang ◽  
Fengjuan Meng ◽  
Cuncai Liu
Keyword(s):  
Porous Medium ◽  
Nonlinear Term ◽  
Index Theory ◽  
Nonlocal Diffusion ◽  
Well Posedness ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Infinite Dimensional ◽  
Long Time ◽  
Porous Medium Equations

In this paper, we mainly consider the well-posedness and long-time behavior of solutions for the nonlocal diffusion porous medium equations with nonlinear term. Firstly, we obtain the well-posedness of the solutions in L1(Ω) for the equations. Secondly, we prove the existence of a global attractor by proving there exists a compact absorbing set. Finally, we apply index theory to consider the dimension of the attractor and prove that there exists an infinite dimensional attractor of the equations under proper conditions.

scholarly journals On global dynamics of 2D convective Cahn–Hilliard equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiaopeng Zhao
Keyword(s):  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Global Dynamics ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Initial Value ◽  
Hilliard Equation ◽  
Long Time ◽  
Cahn Hilliard Equation ◽  
Initial Boundary Value

AbstractIn this paper, we study the long time behavior of solution for the initial-boundary value problem of convective Cahn–Hilliard equation in a 2D case. We show that the equation has a global attractor in $H^{4}(\Omega )$ H 4 ( Ω ) when the initial value belongs to $H^{1}(\Omega )$ H 1 ( Ω ) .

The coupled Cahn–Hilliard/Allen–Cahn system with dynamic boundary conditions

2021 ◽  
pp. 1-27
Author(s):  
Ahmad Makki ◽  
Alain Miranville ◽  
Madalina Petcu
Keyword(s):  
Fractal Dimension ◽  
Boundary Conditions ◽  
Well Posedness ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Dynamic Boundary Conditions ◽  
Finite Dimensional ◽  
Dynamic Boundary ◽  
Long Time ◽  
Finite Fractal Dimension

In this article, we are interested in the study of the well-posedness as well as of the long time behavior, in terms of finite-dimensional attractors, of a coupled Allen–Cahn/Cahn–Hilliard system associated with dynamic boundary conditions. In particular, we prove the existence of the global attractor with finite fractal dimension.

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