By Michael Schulz
This systematic ebook covers in easy language the actual foundations of evolution equations, stochastic strategies and generalized grasp equations utilized on advanced financial platforms, aiding to appreciate the big variability of economic markets, buying and selling and communications networks.
Read Online or Download Statistical Physics and Economics: Concepts, Tools, and Applications PDF
Best thermodynamics and statistical mechanics books
The query of the way reversible microscopic equations of movement may end up in irreversible macroscopic behaviour has been one of many principal concerns in statistical mechanics for greater than a century. the elemental concerns have been identified to Gibbs. Boltzmann carried out a truly public debate with Loschmidt and others with no passable solution.
Complex Dynamics of Glass-Forming Liquids: A Mode-Coupling Theory
The ebook comprises the one on hand entire presentation of the mode-coupling idea (MCT) of complicated dynamics of glass-forming beverages, dense polymer melts, and colloidal suspensions. It describes in a self-contained demeanour the derivation of the MCT equations of movement and explains that the latter outline a version for a statistical description of non-linear dynamics.
Statistical thermodynamics and microscale thermophysics
Many interesting new advancements in microscale engineering are in accordance with the applying of conventional ideas of statistical thermodynamics. during this textual content Van Carey bargains a latest view of thermodynamics, interweaving classical and statistical thermodynamic ideas and making use of them to present engineering structures.
- Further Experiments on the Mass of the Electric Carrier in Metals
- Introduction to the renormalization group and critical phenomena
- Nonextensive entropy: Interdisciplinary applications
- Termodinamica
Additional info for Statistical Physics and Economics: Concepts, Tools, and Applications
Example text
109) G0α and the = Gα (Γ0 ) are fixed by the microscopic initial state Γ0 = Γ (t0 ). In other words, the relevant quantities Gα (t) of a given system are unique functions of the initial state, Gα (t) = Gα (t, Γ0 ). To proceed, we should eliminate all irrelevant degrees of freedom contained in the Liouvillian by the use of an appropriate projection formalism. A convenient starting point for this intention is the introduction of a scalar product (A, B). 110) considering the probability distribution function at the initial time t0 .
How reliable are the available data, and how is this uncertainty likely to affect the range of results? These questions have purely economic character. In order to be able to give a sufficient answer, the economist employs a whole line of experiences in addition to possible mathematical solutions delivered from financial mathematics. All of this allows us to say that an economist is mainly interested in finding a rational approach to a given financial problem. However, both the economist and the financial mathematician will have difficulties in combining the specific dynamics of financial data with general properties of complex systems.
In many practical cases, we have to deal with nonlinear Langevin equations. These equations may be derived in a more or less intuitive manner, but they are only rarely based on a real theoretical framework. However, in the case of Markov processes, the Langevin equations can be obtained from the corresponding Fokker–Planck equations. 129): R Y˙ α (t) = aα (Y (t)) + bα,k (Y (t))ηk (t). , R) are linearly independent stochastic functions. Equations of such a type are also denoted as Langevin equations.