1,428 research outputs found
Stability in Distribution of Neutral Stochastic Functional Differential Equations with Infinite Delay
In this paper, we investigate stability in distribution of neutral stochastic
functional differential equations with infinite delay (NSFDEwID) at the state
space
\begin{equation*}
C_{r}=\{{\varphi\in
C((-\infty,0];R^{d}):\|\varphi\|_{r}=\sup_{-\infty<\theta\leq0}e^{r\theta}\lvert\varphi(\theta)\rvert}
0 \}.
\end{equation*}
We drive a sufficient strong monotone condition for the existence and
uniqueness of the global solutions of NSFDEwID in the state space . We
also address the stability of the solution map and illustrate the
theory with an example.Comment: arXiv admin note: text overlap with arXiv:1805.1067
Stationary Distributions for Retarded Stochastic Differential Equations without Dissipativity
Retarded stochastic differential equations (SDEs) constitute a large
collection of systems arising in various real-life applications. Most of the
existing results make crucial use of dissipative conditions. Dealing with "pure
delay" systems in which both the drift and the diffusion coefficients depend
only on the arguments with delays, the existing results become not applicable.
This work uses a variation-of-constants formula to overcome the difficulties
due to the lack of the information at the current time. This paper establishes
existence and uniqueness of stationary distributions for retarded SDEs that
need not satisfy dissipative conditions. The retarded SDEs considered in this
paper also cover SDEs of neutral type and SDEs driven by L\'{e}vy processes
that might not admit finite second moments.Comment: page 2
Existence and Uniqueness of Mild Solutions to Neutral SFDE driven by a Fractional Brownian Motion with non-Lipschitz Coefficients
The article presents results on existence and uniqueness of mild solutions to
a class of non linear neutral stochastic functional differential equations
(NSFDEs) driven by Fractional Brownian motion in a Hilbert space with
non-Lipschitzian coefficients. The results are obtained by using the method of
Picard approximation.Comment: 13 page
Approximate controllability results for fractional semilinear integro-differential inclusions in Hilbert spaces
In this paper, we consider a class of fractional integro-differential
inclusions in Hilbert spaces. This paper deals with the approximate
controllability for a class of fractional integro-differential control systems.
First, we establishes a set of sufficient conditions for the approximate
controllability for a class of fractional semilinear integro-differential
inclusions in Hilbert spaces. We use Bohnenblust-Karlin's fixed point theorem
to prove our main results. Further, we extend the result to study the
approximate controllability concept with nonlocal conditions. An example is
also given to illustrate our main results.Comment: arXiv admin note: substantial text overlap with arXiv:1502.0008
On a nonlinear neutral stochastic functional integro-differential equation driven by fractional Brownian motion
In this paper, we study the existence and uniqueness of mild solution for a
stochastic neutral partial functional integro-differential equation with delay
in a Hilbert space driven by a fractional Brownian motion and with
non-deterministic diffusion coefficient. We suppose that the linear part has a
resolvent operator. We also establish a sufficient condition for the existence
of the density of a function of the solution. An example is provided to
illustrate the results of this wor
Time-dependent Neutral stochastic functional differential equation driven by a fractional Brownian motion in a Hilbert space
In this paper we consider a class of time-dependent neutral stochastic
functional differential equations with finite delay driven by a fractional
Brownian motion in a Hilbert space. We prove an existence and uniqueness result
for the mild solution by means of the Banach fixed point principle. A practical
example is provided to illustrate the viability of the abstract result of this
work.Comment: 20 pages. arXiv admin note: text overlap with arXiv:1312.668
Exponential Mixing for Retarded Stochastic Differential Equations
In this paper, we discuss exponential mixing property for Markovian
semigroups generated by segment processes associated with several class of
retarded Stochastic Differential Equations (SDEs) which cover SDEs with
constant/variable/distributed time-lags. In particular, we investigate the
exponential mixing property for (a) non-autonomous retarded SDEs by the
Arzel\`{a}--Ascoli tightness characterization of the space \C equipped with
the uniform topology (b) neutral SDEs with continuous sample paths by a
generalized Razumikhin-type argument and a stability-in-distribution approach
and (c) jump-diffusion retarded SDEs by the Kurtz criterion of tightness for
the space \D endowed with the Skorohod topology.Comment: 20 page
Invariant Measures for Dissipative Dynamical Systems: Abstract Results and Applications
In this work we study certain invariant measures that can be associated to
the time averaged observation of a broad class of dissipative semigroups via
the notion of a generalized Banach limit. Consider an arbitrary complete
separable metric space which is acted on by any continuous semigroup
. Suppose that possesses a global
attractor . We show that, for any generalized Banach limit
and any distribution of initial
conditions , that there exists an invariant probability measure
, whose support is contained in , such that for all
observables living in a suitable function space of continuous mappings
on .
This work is based on a functional analytic framework simplifying and
generalizing previous works in this direction. In particular our results rely
on the novel use of a general but elementary topological observation, valid in
any metric space, which concerns the growth of continuous functions in the
neighborhood of compact sets. In the case when does not
possess a compact absorbing set, this lemma allows us to sidestep the use of
weak compactness arguments which require the imposition of cumbersome weak
continuity conditions and limits the phase space to the case of a reflexive
Banach space. Two examples of concrete dynamical systems where the semigroup is
known to be non-compact are examined in detail.Comment: To appear in Communications in Mathematical Physic
Pseudo asymptotically periodic solutions for fractional integro-differential neutral equations
In this paper, we study the existence and uniqueness of pseudo
-asymptotically -periodic mild solutions of class for fractional
integro-differential neutral equations. An example is presented to illustrate
the application of the abstract results.Comment: It has been accepted for publication in SCIENCE CHINA Mathematic
Asymptotic Log-Harnack Inequality and Applications for Stochastic Systems of Infinite Memory
The asymptotic log-Harnack inequality is established for several different
models of stochastic differential systems with infinite memory: non-degenerate
SDEs, Neutral SDEs, semi-linear SPDEs, and stochastic Hamiltonian systems.
As applications, the following properties are derived for the associated
segment Markov semigroups: asymptotic heat kernel estimate; uniqueness of the
invariant probability measure; asymptotic gradient estimate and hence,
asymptotically strong Feller property; and asymptotic irreducibilty.Comment: 24 page
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