Stochastic Integration Techniques

2021 ◽  
pp. 179-193
Keyword(s):  
Stochastic Integration ◽  
Integration Techniques

scholarly journals Quadrature Integration Techniques for Random Hyperbolic PDE Problems

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 160
Author(s):  
Rafael Company ◽  
Vera N. Egorova ◽  
Lucas Jódar
Keyword(s):  
Numerical Methods ◽  
Laplace Transform ◽  
Quadrature Rule ◽  
Inverse Laplace Transform ◽  
Process Time ◽  
Efficient Computation ◽  
Hyperbolic Pde ◽  
Numerical Convergence ◽  
Laplace Transform Technique ◽  
Integration Techniques

In this paper, we consider random hyperbolic partial differential equation (PDE) problems following the mean square approach and Laplace transform technique. Randomness requires not only the computation of the approximating stochastic processes, but also its statistical moments. Hence, appropriate numerical methods should allow for the efficient computation of the expectation and variance. Here, we analyse different numerical methods around the inverse Laplace transform and its evaluation by using several integration techniques, including midpoint quadrature rule, Gauss–Laguerre quadrature and its extensions, and the Talbot algorithm. Simulations, numerical convergence, and computational process time with experiments are shown.

Variations on a theme – Euler and the logsine integral

2012 ◽  
Vol 96 (537) ◽  
pp. 451-458 ◽  
Author(s):  
Nick Lord
Keyword(s):  
Numerical Integration ◽  
Integration Techniques ◽  
Image Position ◽  
Variations On A Theme ◽  
Standard Integration

This article concerns the evaluation of the ‘logsine’ integralWe shall encounter it in several guises. Indeed, standard integration techniques used below readily show that (1) has the same value as the following integrals:En passant, it is worth noting that forms (6) and (7) are the best behaved for numerical integration.I first met the logsine integral as a callow youth in that strange hinterland of results that you may not have met at school but were not guaranteed to meet later on either.

Stochastic integration for set-indexed processes

2000 ◽  
Vol 118 (1) ◽  
pp. 157-181 ◽  
Author(s):  
Ely Merzbach ◽  
Diane Saada
Keyword(s):  
Stochastic Integration

Crisp and Fuzzy Optimisation Approaches for Water Network Retrofit

2007 ◽  
Vol 2 (3) ◽  
Author(s):  
Seingheng Hul ◽  
Denny K. S. Ng ◽  
Raymond R Tan ◽  
Choon-Lai Chiang ◽  
Dominic C. Y. Foo
Keyword(s):  
Linear Programming ◽  
Water Reuse ◽  
Process Integration ◽  
Paper Mill ◽  
Mixed Integer ◽  
Network Synthesis ◽  
Water Recovery ◽  
Water Network ◽  
Real Process ◽  
Integration Techniques

Material reuse/recycle has gained much attention in recent years for both economic and environmental reasons. Process integration techniques for water network synthesis have evolved rapidly in the past decade. With in-plant water reuse/recycle, fresh water and wastewater flowrates are reduced simultaneously. In this work, linear programming and mixed integer linear programming models that include piping cost and process constraints are developed to retrofit an existing water network in a paper mill that was not originally designed with process integration techniques. Five scenarios are presented, each representing different aspects of decision-making in real process integration projects. The fifth scenario makes use of fuzzy optimisation to achieve a compromise solution that considers the inherent conflict between maximising water recovery and minimising capital cost for retrofit.

scholarly journals PROPER CURVATURE COLLINEATIONS IN NONSTATIC SPHERICALLY SYMMETRIC SPACE–TIMES

2008 ◽  
Vol 23 (05) ◽  
pp. 749-759 ◽  
Author(s):  
GHULAM SHABBIR ◽  
M. RAMZAN
Keyword(s):  
Symmetric Space ◽  
Vector Fields ◽  
Killing Vector ◽  
Spherically Symmetric ◽  
Killing Vector Fields ◽  
Infinite Dimensional ◽  
Riemann Matrix ◽  
Integration Techniques ◽  
Curvature Collineations ◽  
Proper Curvature

A study of nonstatic spherically symmetric space–times according to their proper curvature collineations is given by using the rank of the 6×6 Riemann matrix and direct integration techniques. Studying proper curvature collineations in each case of the above space–times it is shown that when the above space–times admit proper curvature collineations, they turn out to be static spherically symmetric and form an infinite dimensional vector space. In the nonstatic cases curvature collineations are just Killing vector fields.

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