Related papers: Probabilities of competing binomial random variabl…
Probabilistic game structures combine both nondeterminism and stochasticity, where players repeatedly take actions simultaneously to move to the next state of the concurrent game. Probabilistic alternating simulation is an important tool to…
An urn contains black and red balls. Let $Z_n$ be the proportion of black balls at time $n$ and $0\leq L<U\leq 1$ random barriers. At each time $n$, a ball $b_n$ is drawn. If $b_n$ is black and $Z_{n-1}<U$, then $b_n$ is replaced together…
We describe a new class of self-similar symmetric $\alpha$-stable processes with stationary increments arising as a large time scale limit in a situation where many users are earning random rewards or incurring random costs. The resulting…
In the game of Matching Pennies, Alice and Bob each hold a penny, and at every tick of the clock they simultaneously display the head or the tail sides of their coins. If they both display the same side, then Alice wins Bob's penny; if they…
Often times, a candidate's attractiveness is directly associated with his clear ideologies and opinions on various policies and social issues. Using the ideas of stochastic differential equations and Ornstein-Uhlenbeck Process, we develop a…
It is shown that an equiprobability hypothesis leads to a scenario in which it is possible to predict the outcome of a single toss of a fair coin with a success probability greater than 50%. We discuss whether this hypothesis might be…
This paper develops systematic approaches to obtain $f$-divergence inequalities, dealing with pairs of probability measures defined on arbitrary alphabets. Functional domination is one such approach, where special emphasis is placed on…
The paper is concerned with asymptotic properties of the principal components analysis of functional data. The currently available results assume the existence of the fourth moment. We develop analogous results in a setting which does not…
Finding a counterfeit coin with the different weight from a set of visually identical coin using a balance, usually a two-armed balance, known as the balance question, is an intersting and inspiring question. Its variants involve…
We are concerned with random ordinary differential equations (RODEs). Our main question of interest is how uncertainties in system parameters propagate through the possibly highly nonlinear dynamical system and affect the system's…
Phase transitions generically occur in random matrix models as the parameters in the joint probability distribution of the random variables are varied. They affect all main features of the theory and the interpretation of statistical models…
Several sub-diffusive stochastic processes in nature, e.g., motion of tagged monomer in polymers, height fluctuation of interfaces and particle dynamics in single-file diffusion etc. can be described rigorously or approximately by the…
Several Artificial Intelligence schemes for reasoning under uncertainty explore either explicitly or implicitly asymmetries among probabilities of various states of their uncertain domain models. Even though the correct working of these…
We propose a strategy for achieving maximum cooperation in evolutionary games on complex networks. Each individual is assigned a weight that is proportional to the power of its degree, where the exponent alpha is an adjustable parameter…
A principled approach to cyclicality and intransitivity in paired comparison data is developed. The proposed methodology enables more precise estimation of the underlying preference profile and facilitates the identification of all cyclic…
Effects associated in quantum mechanics with a divisible probability wave are explained as physically real consequences of the equal but opposite reaction of the apparatus as a particle is measured. Taking as illustration a Mach-Zehnder…
Certain monotonicity properties of the Poisson approximation to the binomial distribution are established. As a natural application of these results, exact (rather than approximate) tests of hypotheses on an unknown value of the parameter…
The probabilities of point events in space 3 + 1 obey an equation of Dirac type. Masses, moments, energies, spins, etc. are the parameters of the probability distribution of such events. The terms and equations of quark-gluon theories turn…
Information in the form of data, which can be stored and transferred between users, can be viewed as an intangible commodity, which can be traded in exchange for money. Determining the fair price at which a string of data should be traded…
Recently a new type of Kramers-Fokker-Planck Equation has been proposed [R. Friedrich et al. Phys. Rev. Lett. {\bf 96}, 230601 (2006)] describing anomalous diffusion in external potentials. In the present paper the explicit cases of a…