Stochastic parallel translation for Riemannian Brownian motion conditioned to hit a fixed point of a sphere

1988 ◽  
pp. 203-210 ◽  
Author(s):  
Ming Liao ◽  
Mark Pinsky
Keyword(s):  
Fixed Point ◽  
Brownian Motion ◽  
Parallel Translation

Global attracting sets of neutral stochastic functional integro-differential equations driven by a fractional Brownian motion

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
A. Bakka ◽  
S. Hajji ◽  
D. Kiouach
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Brownian Motion ◽  
Differential Equations ◽  
Fractional Brownian Motion ◽  
Sufficient Conditions ◽  
Integrodifferential Equations ◽  
Hurst Parameter ◽  
Fixed Point Principle ◽  
Stochastic Functional

Abstract By means of the Banach fixed point principle, we establish some sufficient conditions ensuring the existence of the global attracting sets of neutral stochastic functional integrodifferential equations with finite delay driven by a fractional Brownian motion (fBm) with Hurst parameter H ∈ ( 1 2 , 1 ) {H\in(\frac{1}{2},1)} in a Hilbert space.

scholarly journals On Random Periodic Solution to a Neutral Stochastic Functional Differential Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Lili Gao ◽  
Litan Yan
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Fixed Point ◽  
Brownian Motion ◽  
Functional Differential Equation ◽  
Existence And Uniqueness ◽  
Banach Fixed Point Theorem ◽  
Stochastic Functional Differential Equation ◽  
Functional Differential ◽  
Stochastic Functional

In this paper, we consider the random periodic solution to a neutral stochastic functional differential equation driven by Brownian motion. We obtain the existence and uniqueness of the random periodic solution by Banach fixed point theorem. Moreover, we introduce two examples to illustrate our results.

scholarly journals Transportation Inequalities for Coupled Fractional Stochastic Evolution Equations Driven by Fractional Brownian Motion

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Wentao Zhan ◽  
Yuanyuan Jing ◽  
Liping Xu ◽  
Zhi Li
Keyword(s):  
Fixed Point ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Mild Solution ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Hurst Parameter ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Uniform Distance

In this paper, we consider the existence and uniqueness of the mild solution for a class of coupled fractional stochastic evolution equations driven by the fractional Brownian motion with the Hurst parameter H∈1/4,1/2. Our approach is based on Perov’s fixed-point theorem. Furthermore, we establish the transportation inequalities, with respect to the uniform distance, for the law of the mild solution.

Existence results for systems of coupled impulsive neutral functional differential equations driven by a fractional Brownian motion and a Wiener process

2019 ◽  
Vol 27 (4) ◽  
pp. 225-242
Author(s):  
Tayeb Blouhi ◽  
Mohamed Ferhat
Keyword(s):  
Fixed Point ◽  
Brownian Motion ◽  
Wiener Process ◽  
Existence And Uniqueness ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Existence Results ◽  
Neutral Functional Differential Equations ◽  
Fractional Brownian Motions ◽  
Functional Differential

Abstract In this paper, we prove some results on the existence and uniqueness of mild solutions for a system of semilinear impulsive differentials with infinite fractional Brownian motions and a Wiener process. Our approach is based on a new version of fixed point theorem, due to Krasnoselskii, in generalized Banach spaces.

Noninstantaneous impulsive and nonlocal Hilfer fractional stochastic integrodifferential equations with fractional Brownian motion and Poisson jumps

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Hamdy M. Ahmed ◽  
Mahmoud M. El-Borai ◽  
Mohamed E. Ramadan
Keyword(s):  
Fixed Point ◽  
Brownian Motion ◽  
Fixed Point Theorem ◽  
Fractional Calculus ◽  
Fractional Brownian Motion ◽  
Mild Solution ◽  
Stochastic Analysis ◽  
Integrodifferential Equations ◽  
Poisson Jumps ◽  
New Class

AbstractIn this paper, we introduce the mild solution for a new class of noninstantaneous and nonlocal impulsive Hilfer fractional stochastic integrodifferential equations with fractional Brownian motion and Poisson jumps. The existence of the mild solution is derived for the considered system by using fractional calculus, stochastic analysis and Sadovskii’s fixed point theorem. Finally, an example is also given to show the applicability of our obtained theory.

scholarly journals Brownian motion parametrized with metric space of constant curvature

1981 ◽  
Vol 82 ◽  
pp. 131-140 ◽  
Author(s):  
Shigeo Takenaka ◽  
Izumi Kubo ◽  
Hajime Urakawa
Keyword(s):  
Fixed Point ◽  
Brownian Motion ◽  
Parameter Space ◽  
Metric Space ◽  
Random Variable ◽  
Time Parameter ◽  
Space Of Constant Curvature ◽  
Mouvement Brownien ◽  
The Difference ◽  
Gaussian System

P. Lévy introduced a generalized notion of Brownian motion in his monograph “Processus stochastiques et mouvement brownien” by taking the time parameter space to be a general metric space. Let (M, d) be a metric space and let O be a fixed point of M called the origin. Following his definition, a Brownian motion parametrized with the metric space (M, d) is a Gaussian system ℬ = {B(m); m ∈ M} such that the difference B(m) − B(m′) is a random variable with mean zero and variance d(m, m′), and that B(O) = 0.

scholarly journals The Existence, Uniqueness, and Controllability of Neutral Stochastic Delay Partial Differential Equations Driven by Standard Brownian Motion and Fractional Brownian Motion

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Dehao Ruan ◽  
Jiaowan Luo
Keyword(s):  
Fixed Point ◽  
Brownian Motion ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Brownian Motion ◽  
Fixed Point Method ◽  
Standard Brownian Motion ◽  
Partial Differential ◽  
Stochastic Delay ◽  
Delay Partial Differential Equations

We focus on a class of neutral stochastic delay partial differential equations perturbed by a standard Brownian motion and a fractional Brownian motion. Under some suitable assumptions, the existence, uniqueness, and controllability results for these equations are investigated by means of the Banach fixed point method. Moreover, an example is presented to illustrate our main results.

scholarly journals Existence and exponential stability of almost pseudo automorphic solution for neutral stochastic evolution equations driven by G-Brownian motion

Filomat ◽  
2020 ◽  
Vol 34 (4) ◽  
pp. 1075-1092
Author(s):  
Pengju Duan
Keyword(s):  
Fixed Point ◽  
Brownian Motion ◽  
Exponential Stability ◽  
Mild Solution ◽  
Existence And Uniqueness ◽  
Evolution Operator ◽  
Evolution Equations ◽  
Sufficient Conditions ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations

This paper mainly concerns the quasi sure exponential stability of square mean almost pseudo automorphic mild solution for a class of neutral stochastic evolution equations driven by G-Brownian motion. By means of evolution operator theorem and fixed point theorem, existence and uniqueness of square mean almost pseudo automorphic mild solution is obtained. Also, a series of sufficient conditions on exponential stability and quasi sure exponential stability are established.

scholarly journals Stability of a Class of Impulsive Neutral Stochastic Functional Partial Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Yue Liu ◽  
Dehao Ruan
Keyword(s):  
Fixed Point ◽  
Brownian Motion ◽  
Partial Differential Equations ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Exponential Stability ◽  
Partial Differential ◽  
The Fixed Point Theorem ◽  
Moment Exponential Stability ◽  
Stochastic Functional

In this paper, a class of impulsive neutral stochastic functional partial differential equations driven by Brownian motion and fractional Brownian motion is investigated. Under some suitable assumptions, the pth moment exponential stability is discussed by means of the fixed-point theorem. Our results also improve and generalize some previous studies. Moreover, one example is given to illustrate our main results.

scholarly journals Controllability of impulsive neutral stochastic integro-differential systems driven by fractional Brownian motion with delay and Poisson jumps

2021 ◽  
Author(s):  
Youssef Benkabdi ◽  
Lakhel El Hassan
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Stochastic Analysis ◽  
Separable Hilbert Space ◽  
Infinite Delay ◽  
Poisson Jumps ◽  
Differential Systems ◽  
Controllability Result

In this paper the controllability of a class of impulsive neutral stochastic integro-differential systems driven by fractional Brownian motion and Poisson process in a separable Hilbert space with infinite delay is studied. The controllability result is obtained by using stochastic analysis and a fixed-point strategy. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained result.

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