scholarly journals Hermite-Hadamard type inequalities for p-convex stochastic processes

2019 ◽  
Vol 9 (2) ◽  
pp. 148-153 ◽  
Author(s):  
Nurgul Okur ◽  
Imdat Işcan ◽  
Emine Yuksek Dizdar
Keyword(s):  
Stochastic Process ◽  
Mathematical Programming ◽  
Stochastic Processes ◽  
Mean Square ◽  
Important Place ◽  
Mathematical Programming Problems ◽  
Square Integrability ◽  
Convex Stochastic Processes ◽  
Convex Stochastic Process

In this study are investigated p-convex stochastic processes which are extensions of convex stochastic processes. A suitable example is also given for this process. In addition, in this case a p-convex stochastic process is increasing or decreasing, the relation with convexity is revealed. The concept of inequality as convexity has an important place in literature, since it provides a broader setting to study the optimization and mathematical programming problems. Therefore, Hermite-Hadamard type inequalities for p-convex stochastic processes and some boundaries for these inequalities are obtained in present study. It is used the concept of mean-square integrability for stochastic processes to obtain the above mentioned results.

scholarly journals Generalized Fractional Inequalities of the Hermite–Hadamard Type for Convex Stochastic Processes

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
McSylvester Ejighikeme Omaba ◽  
Eze R. Nwaeze
Keyword(s):  
Stochastic Process ◽  
Integral Operator ◽  
Stochastic Processes ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Fractional Integrals ◽  
Convex Stochastic Processes ◽  
Katugampola Fractional Integral ◽  
Convex Stochastic Process

AbstractA generalization of the Hermite–Hadamard (HH) inequality for a positive convex stochastic process, by means of a newly proposed fractional integral operator, is hereby established. Results involving the Riemann– Liouville, Hadamard, Erdélyi–Kober, Katugampola, Weyl and Liouville fractional integrals are deduced as particular cases of our main result. In addition, we also apply some known HH results to obtain some estimates for the expectations of integrals of convex and p-convex stochastic processes. As a side note, we also pointed out a mistake in the main result of the paper [Hermite–Hadamard type inequalities, convex stochastic processes and Katugampola fractional integral, Revista Integración, temas de matemáticas 36 (2018), no. 2, 133–149]. We anticipate that the idea employed herein will inspire further research in this direction.

scholarly journals Analytic-Numerical Solution of Random Parabolic Models: A Mean Square Fourier Transform Approach

2018 ◽  
Vol 23 (1) ◽  
pp. 79-100 ◽  
Author(s):  
Maria-Consuelo Casaban ◽  
Juan-Carlos Cortes ◽  
Lucas Jodar
Keyword(s):  
Stochastic Process ◽  
Fourier Transform ◽  
Standard Deviation ◽  
Stochastic Processes ◽  
Numerical Solution ◽  
Integral Form ◽  
Initial Condition ◽  
Mean Square ◽  
Improper Integrals ◽  
Gauss Hermite Quadrature

This paper deals with the construction of mean square analytic-numerical solution of parabolic partial differential problems where both initial condition and coefficients are stochastic processes. By using a random Fourier transform, an inf- nite integral form of the solution stochastic process is firstly obtained. Afterwards, explicit expressions for the expectation and standard deviation of the solution are obtained. Since these expressions depend upon random improper integrals, which are not computable in an exact manner, random Gauss-Hermite quadrature formulae are introduced throughout an illustrative example.

scholarly journals Mean Square Integral Inequalities for Generalized Convex Stochastic Processes via Beta Function

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Putian Yang ◽  
Shiqing Zhang
Keyword(s):  
Applied Sciences ◽  
Stochastic Processes ◽  
Beta Function ◽  
Integral Inequalities ◽  
Mean Square ◽  
Convex Stochastic Processes

The integral inequalities have become a very popular area of research in recent years. The present paper deals with some important generalizations of convex stochastic processes. Several mean square integral inequalities are derived for this generalization. The involvement of the beta function in the results makes the inequalities more convenient for applied sciences.

An Application of Mean Square Calculus to Sliding Wear

2009 ◽  
Vol 77 (2) ◽  
Author(s):  
Cláudio R. Ávila da Silva ◽  
Giuseppe Pintaude ◽  
Hazim Ali Al-Qureshi ◽  
Marcelo Alves Krajnc
Keyword(s):  
Stochastic Process ◽  
Stochastic Processes ◽  
Sliding Wear ◽  
Random Variables ◽  
Random Variable ◽  
Expected Value ◽  
Mean Square ◽  
Cauchy Problems ◽  
Numerical Examples ◽  
Correlation Models

In this paper the Archard model and classical results of mean square calculus are used to derive two Cauchy problems in terms of the expected value and covariance of the worn height stochastic process. The uncertainty is present in the wear and roughness coefficients. In order to model the uncertainty, random variables or stochastic processes are used. In the latter case, the expected value and covariance of the worn height stochastic process are obtained for three combinations of correlation models for the wear and roughness coefficients. Numerical examples for both models are solved. For the model based on a random variable, a larger dispersion in terms of worn height stochastic process was observed.

scholarly journals Quantum Hermite-Hadamard type integral inequalities for convex stochastic processes

2021 ◽  
Vol 6 (11) ◽  
pp. 11989-12010
Author(s):  
Thanin Sitthiwirattham ◽  
◽  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Saowaluck Chasreechai ◽  
...  
Keyword(s):  
Stochastic Processes ◽  
Integral Inequalities ◽  
Mean Square ◽  
Type Integral ◽  
Convex Stochastic Processes

<abstract><p>In this paper, we introduce the notions of $ q $-mean square integral for stochastic processes and co-ordinated stochastic processes. Furthermore, we establish some new quantum Hermite-Hadamard type inequalities for convex stochastic processes and co-ordinated stochastic processes via newly defined integrals. It is also revealed that the results presented in this research transformed into some already proved results by considering the limits as $ q, \; q_{1}, \; q_{2}\rightarrow 1^{-} $ in the newly obtained results.</p></abstract>

scholarly journals Stochastic Processes with a Particular Type of Variograms

2007 ◽  
Vol 2007 ◽  
pp. 1-5 ◽  
Author(s):  
Chunsheng Ma
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Stochastic Processes ◽  
Series Expansion ◽  
Real Line ◽  
Random Fields ◽  
The Other ◽  
Simple Construction ◽  
The Real ◽  
Line Form

This paper is concerned with a class of stochastic processes or random fields with second-order increments, whose variograms have a particular form, among which stochastic processes having orthogonal increments on the real line form an important subclass. A natural issue, how big this subclass is, has not been explicitly addressed in the literature. As a solution, this paper characterizes a stochastic process having orthogonal increments on the real line in terms of its variogram or its construction. Our findings are a little bit surprising: this subclass is big in terms of the variogram, and on the other hand, it is relatively “small” according to a simple construction. In particular, every such process with Gaussian increments can be simply constructed from Brownian motion. Using the characterizations we obtain a series expansion of the stochastic process with orthogonal increments.

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