Stochastic Processes In Project Management

Performance of planned activities not always leads to the achievement of planned results in innovation projects with a high degree of uncertainty. Management of such specific projects requires the usage of specific methods and processes. It is necessary to develop own stochastic process methods rather than use classical methods of deterministic management. The main peculiarity of stochastic processes of projects consists in the inability to carry out more than one experiment. Implementation of a project is a stochastic process, which is carried out only once. For the purposes of the research, stochastic project management is the process of organisation, planning and control over projects, in which the decisions and actions of managers are described by stochastic functions. If the project realisation is described by stochastic processes, the project management process is indeed described by stochastic processes. This research suggests a project management approach based on the focus on the project product and project management as stochastic processes based on stochastic functions. It is demonstrated that stochastic function values, which underlie the stochastic processes, are formed by the intellectual instruments of those involved in the project and are developed on the basis of their knowledge and skills. The latter, in turn, are the result of studying and practical work on the project. Therefore, it is difficult to predict decisions and actions of managers and contractors, even if internal and external influences on them are specified. Then, any decisions or actions of such persons with regard to the external observer are described by stochastic functions. The purpose of this study is to describe the processes of stochastic project management. The purpose of the study is the project management process. The subject of research is the methods of stochastic project management. Within the framework of the study, all groups of processes of stochastic control will be mathematically described and the conditions of their impact determined. The processes of stochastic project management are outlined and formally presented. These are the processes of project management organisation, the processes of project management support, processes of project content definition, processes of defining the resources, required for the project works, processes of project planning, processes of influence on contractors of actions (works)

Temperley-Lieb Stochastic Processes

We discuss one-dimensional stochastic processes defined through the Temperley-Lieb algebra related to the Q=1 Potts model. For various boundary conditions, we formulate a conjecture relating the probability distribution which describes the stationary state, to the enumeration of a symmetry class of alternating sign matrices, objects that have received much attention in combinatorics.Comment: 9 pages LaTeX, 11 Postscript figures, minor change

Wavelet entropy of stochastic processes

We compare two different definitions for the wavelet entropy associated to stochastic processes. The first one, the Normalized Total Wavelet Entropy (NTWS) family [Phys. Rev. E 57 (1998) 932; J. Neuroscience Method 105 (2001) 65; Physica A (2005) in press] and a second introduced by Tavares and Lucena [Physica A 357 (2005)~71]. In order to understand their advantages and disadvantages, exact results obtained for fractional Gaussian noise (-1<alpha< 1) and the fractional Brownian motion (1 < alpha < 3) are assessed. We find out that NTWS family performs better as a characterization method for these stochastic processes.Comment: 12 pages, 4 figures, submitted to Physica

Stochastic processes and conformal invariance

We discuss a one-dimensional model of a fluctuating interface with a dynamic exponent $z=1$. The events that occur are adsorption, which is local, and desorption which is non-local and may take place over regions of the order of the system size. In the thermodynamic limit, the time dependence of the system is given by characters of the $c=0$ conformal field theory of percolation. This implies in a rigorous way a connection between CFT and stochastic processes. The finite-size scaling behavior of the average height, interface width and other observables are obtained. The avalanches produced during desorption are analyzed and we show that the probability distribution of the avalanche sizes obeys finite-size scaling with new critical exponents.Comment: 4 pages, 6 figures, revtex4. v2: change of title and minor correction