ترغب بنشر مسار تعليمي؟ اضغط هنا

Generation of random dynamical systems from fractional stochastic delay differential equations

258   0   0.0 ( 0 )
 نشر من قبل Stefan Siegmund
 تاريخ النشر 2013
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

In this note we prove that a fractional stochastic delay differential equation which satisfies natural regularity conditions generates a continuous random dynamical system on a subspace of a Holder space which is separable.



قيم البحث

اقرأ أيضاً

137 - N.D. Cong , H.T. Tuan 2016
We show that any two trajectories of solutions of a one-dimensional fractional differential equation (FDE) either coincide or do not intersect each other. In contrary, in the higher dimensional case, two different trajectories can meet. Furthermore, one-dimensional FDEs and triangular systems of FDEs generate nonlocal fractional dynamical systems, whereas a higher dimensional FDE does, in general, not generate a nonlocal dynamical system.
252 - Bixiang Wang 2014
In this paper, we introduce concepts of pathwise random almost periodic and almost automorphic solutions for dynamical systems generated by non-autonomous stochastic equations. These solutions are pathwise stochastic analogues of deterministic dynami cal systems. The existence and bifurcation of random periodic (random almost periodic, random almost automorphic) solutions have been established for a one-dimensional stochastic equation with multiplicative noise.
78 - Zhenxin Liu 2006
Conley index theory is a very powerful tool in the study of dynamical systems, differential equations and bifurcation theory. In this paper, we make an attempt to generalize the Conley index to discrete random dynamical systems. And we mainly follow the Conley index for maps given by Franks and Richeson in [6]. Furthermore, we simply discuss the relations of isolated invariant sets between time-continuous random dynamical systems and the corresponding time-$h$ maps. For applications we give several examples to illustrate our results.
427 - Miaomiao Fu , Zhenxin Liu 2010
The concept of square-mean almost automorphy for stochastic processes is introduced. The existence and uniqueness of square-mean almost automorphic solutions to some linear and non-linear stochastic differential equations are established provided the coefficients satisfy some conditions. The asymptotic stability of the unique square-mean almost automorphic solution in square-mean sense is discussed.
133 - Xin Liu , Zhenxin Liu 2020
In this paper, we use a unified framework to study Poisson stable (including stationary, periodic, quasi-periodic, almost periodic, almost automorphic, Birkhoff recurrent, almost recurrent in the sense of Bebutov, Levitan almost periodic, pseudo-peri odic, pseudo-recurrent and Poisson stable) solutions for semilinear stochastic differential equations driven by infinite dimensional Levy noise with large jumps. Under suitable conditions on drift, diffusion and jump coefficients, we prove that there exist solutions which inherit the Poisson stability of coefficients. Further we show that these solutions are globally asymptotically stable in square-mean sense. Finally, we illustrate our theoretical results by several examples.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا