The Probability Flow in the Stock Market and Spontaneous Symmetry Breaking in Quantum Finance

The spontaneous symmetry breaking phenomena applied to Quantum Finance considers that the martingale state in the stock market corresponds to a ground (vacuum) state if we express the financial equations in the Hamiltonian form. The original analysis for this phenomena completely ignores the kinetic terms in the neighborhood of the minimal of the potential terms. This is correct in most of the cases. However, when we deal with the martingale condition, it comes out that the kinetic terms can also behave as potential terms and then reproduce a shift on the effective location of the vacuum (martingale). In this paper, we analyze the effective symmetry breaking patterns and the connected vacuum degeneracy for these special circumstances. Within the same scenario, we analyze the connection between the flow of information and the multiplicity of martingale states, providing in this way powerful tools for analyzing the dynamic of the stock markets.

The coupled gravity of straight space-time and uncertainty principle

This article points out that when the boundary condition $\frac{T}{T_{c}}=z$ (when z is a complex number) is preset, bosons can produce Bose condensation without an energy layer. Under Bose condensation, incident waves may condense in various black holes in the theory of loop quantum gravity. This paper shows that under the gravitational subsystem composed of two bosons, the extreme value of the measurement uncertainty principle can be smaller because the probability flow density is related to the time parameter. This is a model to verify the existence of gravitons.

Nonparametric Versus Parametric Reasoning Based on Contingency Tables

This paper proposes scenarios of generating two-way and three way contingency tables (CTs). A concept of probability flow parameter (PFP) plays a crucial role in these scenarios. Additionally, measures of untruthfulness of H0 are defined. The power divergence statistics and the |X| statistics are used. This paper is a simple attempt to replace a nonparametric statistical inference from CTs by the parametric one. Maximum likelihood method is applied to estimate PFP and instructions of generating CTs according to scenarios in question are presented. The Monte Carlo method is used to carry out computer simulations.

The convergense rate of stationary distribution of retrial queueing system with queue

This paper describes a steady state behavior of the retrial system in the case of one server, one place in the queue and an infinity orbit. We research Markov`s models of retrial systems and variable rate of input flow controlled by threshold strategy. We defined stationary regime existence conditions and investigated probability characteristics of process for two-dimension Markov process with continuous time which we took as a main model of the specified system. In stationary regime for probability characteristics of the service process were found explicit formulas. Research methods which we used are based on the initial process approximation by the process with bounded state space. Results of the research allow us to evaluate convergence rates of stationary distribution of finite systems with repeated calls to stationary distribution of infinite systems. Method of probability flow equating is used for obtain explicit expressions for stationary system probabilities through the closed path which are defined in a special way. We considered model for one service devices and one place in the queue, which are controlled by threshold strategies.