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3) is non-integrable if and only if a = 0 and d ] 1 , 0[ 2 For this latter case, (X(t)) is a long memory process From the covariance behavior at in nity, we can also deduce that the process (X(t)) is strongly mixing if and only if a < 0 As in the discrete case, there are various memory-mixing scenarios The regularity of the sample path is determined by the covariance behavior at the origin: 1) if D < 3 , then (t) = (0)+ 1 t2 +o(t2+ ), where 1 is a non-zero constant 2 and a positive number; 2) if D > 3 , then (t) = (0)+ 2 t 2D 1 +o(t 2D 1 ), where 2 is a non-zero 2 constant; 3) if D = 3 , then (t) = (0) + 2

Page 185 The focus was switching from technical matters to budget keeping This development was supported by investments into project management tools, including the development of new project control software When Rauma Offshore Contracting started, it adapted a model where the project manager had a very independent position, being solely responsible for the project, including maintaining the customer interface, performance of the product, schedule, and ensuring the profit Neuvo s basic philosophy was that if project managers were expected to assume a larger responsibility, they also had to have the freedom and power to make the necessary decisions Following the same principle, the project responsibility was further subdivided underneath the project manager among a small team of project discipline engineers On one hand, this was a natural and easy decision The company had limited resources but was aiming for large contracts where practically the whole scope of work was outsourced through the supply chain In a small project team, every individual was responsible for relatively large piece of work and budget, while still working mostly on their own On the other hand, creating a new business model employing strong, independent project managers was also a difficult decision The old company culture did not fully support this approach, and some people were also lacking the skills necessary to run this kind of operation Finally, implementing the model was also at the time difficult because the increased power of the project managers occasionally ran into conflict with the opinions and views of the managing director Mr Neuvo, however, so well understood how dependent the success of his business was on high-profile project managers that he accepted the risk of wrong decisions rather than overruling the project manager in matters that were clearly their responsibility The ISO 9001 quality standard was a good framework for developing Rauma Offshore Contracting s project management systems and procedures Because the resources of the new company.

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t2 2

log t(1 + o(1))

From this, we deduce that there is a process (Y (t)) equivalent to (X(t)), such that all the trajectories are H lderian of exponent for all ]0, min(1, 1 D)[ 2

.

Moreover, if D < 3 these trajectories are of class C 1 The Hausdorff dimension 2 of the sample paths of the process Y (t) is then equal to 1 if D < 3 and to 5 + D 2 2 if D [ 3 , 1 [ In this studied family, there exist long memory processes X(t) 2 2 (a = 0, d ] 1 , 0[), which can be as regular (D < 3 ) or irregular (D close to 2 2 1 ) as desired Conversely, there exist processes X(t) with short memory (a < 0) 2 having arbitrary regularity, in contrast to fractional Brownian motion However, only the processes obtained from F (s) = sd transfer functions are self-similar 85 Distribution processes 851 Motivation and generalization of distribution processes To complement the survey of continuous time fractional ARMA processes, the idea that spontaneously comes to mind is to study the consequences of slackening the constraint D < 0 Then, the impulse response f is no longer a simple function, belonging to L2 , but can be de ned as the inverse Laplace transform of F in the space D of distributions with support on + Expression (811) no longer makes sense and it is necessary to de ne the process X differently Distribution processes were introduced independently by Ito [ITO 54], and Gelfand and Vilenkin [GEL 64] They can be de ned in the following way: a second order distribution process X is a continuous linear application from the space of C test functions with compact support in , to the space of random variables whose moment of second order exists We note: C0 ( ) X( ) = X, L2 ( ) and we have, for all K compact of :

CK , k, C0 (K),

X,

L2 ( )

.

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