It is well-known that the construction of space of probability measures P is functorial in the category Comp of compact Hausdorff spaces. The functor P is normal in the sense of E.V. Shchepin [1]. It is well-known that the functor P is open, i.e. it preserves the class of open surjective maps. This was first proved by Ditor and Eifler [2]. E.V. Shchepin [1] discovered tight relations between th...

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...

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.

In this paper a new stereo algorithm is presented for computing dense disparity maps from stereo image pairs using a cost relaxation approach, where the disparity map is the momentary state of a dynamic system. Following biologically motivated cooperative approaches a disparity space is defined with cooperating probability variables. In a first step a correlation based similarity measure is per...

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 ...

We consider a stochastic N -particle model for the spatially homogeneous Boltzmann evolution and prove its convergence to the associated Boltzmann equation when N −→ ∞. For any time T > 0 we bound the distance between the empirical measure of the particle system and the measure given by the Boltzmann evolution in some homogeneous negative Sobolev space. The control we get is Gaussian, i.e. we p...