This article continues study of the prequential framework for evaluating a probability forecaster. Testing the hypothesis that the sequence of forecasts issued by the forecaster is in agreement with the observed outcomes can be done using prequential notions of probability. It turns out that there are two natural notions of probability in the prequential framework: game-theoretic, whose idea go...

1. Introduction. 4 will denote the space of all plane paths w, so that w is a short way of denoting the curve z(t, (o) = {x(t, w), y(t, (o)} (0 < t < + oc). We assume that there is a probability measure ,u defined on a Borel field 9 of (measurable) subsets of S2, so that the system (Q, 3~ 7_ " u) forms a mathematical model for Brownian paths in the plane. [For details of the definition of ,u, s...

probability of private information based trade (pin) has introduced as information risk measure. this paper is going to estimate probability of private information based trade (pin) in tehran stock exchange using microstructure models. our results show that pin is significantly different from zero for tehran stock exchange.

There are many research available on the study of a real-valued fractal interpolation function and dimension its graph. In this paper, our main focus is to dimensional results for vector-valued Riemann–Liouville fractional integral. Here, we give some which ensure that functions quite different from functions. We determine interesting bounds Hausdorff graph function. also obtain associated inva...

[1] In this study we incorporate the existing concept of fractional mobility into a stochastic framework for modeling the partial transport of mixed-size sediment. The model predicts the fractional transport rates with parameters such as the long-run moving probability, mean particle velocity, and fractional mobility, all varying with the dimensionless effective shear stress. Movement of bed lo...

The returns from a traded security typically have the order of magnitude √ dt. This can be explained by the absence of riskless opportunities for making money: any different order of magnitude would permit such opportunities. The explanation has been made rigorous in the standard measure-theoretic framework for continuous-time probability, but this requires the assumption that the security’s pr...

In this paper we propose a model of …nancial markets in which agents have limited ability to trade and no probability is given from the outset. In the absence of arbitrage opportunities, assets are priced according to a probability measure that lacks countable additivity. Despite …nite additivity, we obtain an explicit representation of the expected value with respect to the pricing measure, ba...

The diameter of a graph is the maximum over vertices u and v of the distance between u and v. It is easy to show that graphs with high conductance must have low diameter. If the set of edges leaving a set must be large relative to the size of the set, then after taking neighborhoods a few times, one must encounter most of the edges. We now make this intuition precise. Recall from Lecture 7 the ...