Based on recent studies by Guy Jumarie [1] which defines probability density of fractional order and fractional moments by using fractional calculus (fractional derivatives and fractional integration), this study expands the concept of probability density of fractional order by defining the fractional probability measure, which leads to a fractional probability theory parallel to the classical ...

This paper examines the impact of tick size reduction on price continuity in the Taiwan stock market where employs call auction method throughout the entire trading day. Using the intraday data from September 1, 2004 to August 31, 2005, the results indicate that the price continuity of call stock market could be improved after tick size reduction. A smaller tick size is associated with a lower ...

Why does classical equilibrium statistical mechanics work? Malament and Zabell (1980) noticed that, for ergodic dynamical systems, the unique absolutely continuous invariant probability measure is the microcanonical. Earman and Rédei (1996) replied that systems of interest are very probably not ergodic, so that absolutely continuous invariant probability measures very distant from the microcano...

In this paper, we study continuity properties in Hausdorff topology for different special set multifunctions. Key–words: set multifunction, multi(sub)measure, regular, exhaustive, increasing/decreasing convergent, order continuity, probability.

the aim of this paper is to show how some measures of noncompactness in the banach space of continuous functions defined on two variables can be applied to the solvability of a general system of functional integral equations . the results obtained generalize and extend several equations . an illustrative example is also presented .

In the paper, we consider the application of the theory of probability metrics in several areas in the field of finance. First, we argue that specially structured probability metrics can be used to quantify stochastic dominance relations. Second, the methods of the theory of probability metrics can be used to arrive at a general axiomatic treatment of dispersion measures and probability metrics...

Abstract We introduce the notions of ? -Baire property and -semiopen set using sets Lebesgue measure zero. For a family A subsets real line, we define ( ? )-property analogously as it was done in category case for )-property. The main result is that all line having has iff situated between Euclidean topology sets.

The stochastic transport equation is considered where the randomness given by a symmetric integral with respect to measure. For measure, only σ-additivity in probability and continuity of paths assumed. Existence uniqueness weak solution are proved.

This paper presents numerical approximation schemes for a two stage stochastic programming problem where the second stage problem has a general nonlinear complementarity constraint: first, the complementarity constraint is approximated by a parameterized system of inequalities with a wellknown regularization approach [44] in deterministic mathematical programs with equilibrium constraints; the ...