Stepanov-Like Pseudo Almost Automorphic Solutions to Some Stochastic Differential Equations

2015 ◽  
Vol 39 (1) ◽  
pp. 181-197 ◽  
Author(s):  
Yong-Kui Chang ◽  
Zhuan-Xia Cheng ◽  
G. M. N’Guérékata
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Almost Automorphic ◽  
Pseudo Almost Automorphic

scholarly journals (Weighted pseudo) almost automorphic solutions in distribution for fractional stochastic differential equations driven by levy noise

Filomat ◽  
2021 ◽  
Vol 35 (7) ◽  
pp. 2403-2424
Author(s):  
Min Yang
Keyword(s):  
Differential Equations ◽  
Fractional Calculus ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Stochastic Analysis ◽  
Contraction Principle ◽  
Lévy Noise ◽  
Almost Automorphic ◽  
Fractional Stochastic Differential Equations ◽  
Pseudo Almost Automorphic

In this paper, by using contraction principle, fractional calculus and stochastic analysis, we study the existence and uniqueness of (weighted pseudo) almost automorphic solutions in distribution for fractional stochastic differential equations driven by L?vy noise. An example is presented to illustrate the application of the abstract results.

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.

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