Existence and global attractiveness of a square-mean μ-pseudo almost automorphic solution for some stochastic evolution equation driven by Lévy noise

2016 ◽  
Vol 290 (8-9) ◽  
pp. 1260-1280 ◽  
Author(s):  
Mamadou Abdoul Diop ◽  
Khalil Ezzinbi ◽  
Mamadou Moustapha Mbaye
Keyword(s):  
Evolution Equation ◽  
Lévy Noise ◽  
Stochastic Evolution Equation ◽  
Stochastic Evolution ◽  
Almost Automorphic ◽  
Pseudo Almost Automorphic ◽  
Levy Noise ◽  
Pseudo Almost Automorphic Solution

scholarly journals Almost automorphic solution for some stochastic evolution equation driven by Lévy noise with coefficients S2−almost automorphic

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Mamadou Moustapha Mbaye
Keyword(s):  
Evolution Equation ◽  
Lévy Noise ◽  
Stochastic Evolution Equation ◽  
Stochastic Evolution ◽  
Almost Automorphic ◽  
Levy Noise

AbstractIn this work we first introduce the concept of Poisson Stepanov-like almost automorphic (Poisson S

scholarly journals Pseudo Almost Automorphic Solutions for Stochastic Differential Equations Driven by Lévy Noise and Its Optimal Control

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1674
Author(s):  
Chao Tang ◽  
Rong Hou
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Stochastic Processes ◽  
Stochastic Differential Equations ◽  
Lévy Noise ◽  
Bounded Interval ◽  
Almost Automorphic ◽  
Pseudo Almost Automorphic ◽  
Levy Noise ◽  
Theoretical Results

As we know, the periodic functions are symmetric within a cycle time, and it is meaningful to generalize the periodicity into more general cases, such as almost periodicity or almost automorphy. In this work, we introduce the concept of Poisson Sγ2-pseudo almost automorphy (or Poisson generalized Stepanov-like pseudo almost automorphy) for stochastic processes, which are almost-symmetric within a suitable period, and establish some useful properties of such stochastic processes, including the composition theorems. In addition, we apply a Krasnoselskii–Schaefer type fixed point theorem to obtain the existence of pseudo almost automorphic solutions in distribution for some semilinear stochastic differential equations driven by Lévy noise under Sγ2-pseudo almost automorphic coefficients. In addition, then we establish optimal control results on the bounded interval. Finally, an example is provided to illustrate the theoretical results obtained in this paper.

Sign in / Sign up

Export Citation Format

Share Document