A Generalization of the M/G/1 Queue
A generalization of Ueno's inequality for n-step transition probabilities
We provide a generalization of Ueno's inequality for n-step transition probabilities of Markov chains in a general state space. Our result is relevant to the study of adaptive control problems and approximation problems in the theory of discrete-time Markov decision processes and stochastic games.
A generalized beta function and associated probability density.
A generalized Biane process
A generalized bivariate lifetime distribution based on parallel-series structures
In this paper, a generalized bivariate lifetime distribution is introduced. This new model is constructed based on a dependent model consisting of two parallel-series systems which have a random number of parallel subsystems with fixed components connected in series. The probability that one system fails before the other one is measured by using competing risks. Using the extreme-value copulas, the dependence structure of the proposed model is studied. Kendall's tau, Spearman's rho and tail dependences...
A generalized Chacon's inequality and order convergence of processes
A generalized fundamental identity
A generalized Itô's formula in two-dimensions and stochastic Lebesgue-Stieltjes integrals.
A generalized Itô-Ventzell formula. Application to a class of anticipating stochastic differential equations
A generalized Kahane-Khinchin inequality
The inequality with an absolute constant C, and similar ones, are extended to the case of belonging to an arbitrary normed space X and an arbitrary compact group of unitary operators on X instead of the operators of multiplication by .
A generalized logistic distribution.
A generalized Markov decision process
A generalized mean-reverting equation and applications
Consider a mean-reverting equation, generalized in the sense it is driven by a 1-dimensional centered Gaussian process with Hölder continuous paths on [0,T] (T> 0). Taking that equation in rough paths sense only gives local existence of the solution because the non-explosion condition is not satisfied in general. Under natural assumptions, by using specific methods, we show the global existence and uniqueness of the solution, its integrability, the continuity and differentiability of the...
A generalized Ostrowski type inequality for a random variable whose probability density function belongs to .
A generalized residual information measure and its properties.
A Geometric Appraoch to Finite Sample and Large Deviation Properties in Two-Way ANOVA with Spherically Distributed Error Vectors.
A geometric approach for convexity in some variational problem in the Gauss space
A geometric approach to correlation inequalities in the plane
By elementary geometric arguments, correlation inequalities for radially symmetric probability measures are proved in the plane. Precisely, it is shown that the correlation ratio for pairs of width-decreasing sets is minimized within the class of infinite strips. Since open convex sets which are symmetric with respect to the origin turn out to be width-decreasing sets, Pitt’s Gaussian correlation inequality (the two-dimensional case of the long-standing Gaussian correlation conjecture) is derived...
A geometric approach to measuring dependence between random vectors
A geometric approach to on-diagonal heat kernel lower bounds on groups
We introduce a new method for obtaining heat kernel on-diagonal lower bounds on non- compact Lie groups and on infinite discrete groups. By using this method, we are able to recover the previously known results for unimodular amenable Lie groups as well as for certain classes of discrete groups including the polycyclic groups, and to give them a geometric interpretation. We also obtain new results for some discrete groups which admit the structure of a semi-direct product or of a wreath product....