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....
A geometric derivation of the linear Boltzmann equation for a particle interacting with a Gaussian random field, using a Fock space approach
In this article the linear Boltzmann equation is derived for a particle interacting with a Gaussian random field, in the weak coupling limit, with renewal in time of the random field. The initial data can be chosen arbitrarily. The proof is geometric and involves coherent states and semi-classical calculus.
A geometrical approach to the special stable distributions
A geometry on the space of probabilities (II). Projective spaces and exponential families.
In this note we continue a theme taken up in part I, see [Gzyl and Recht: The geometry on the class of probabilities (I). The finite dimensional case. Rev. Mat. Iberoamericana 22 (2006), 545-558], namely to provide a geometric interpretation of exponential families as end points of geodesics of a non-metric connection in a function space. For that we characterize the space of probability densities as a projective space in the class of strictly positive functions, and these will be regarded as a...
A graph method for Markov models solving
A Green's Function for Non-Homogegeous Random Walks on Free Products.
A growth estimate for continuous random fields
We prove a polynomial growth estimate for random fields satisfying the Kolmogorov continuity test. As an application we are able to estimate the growth of the solution to the Cauchy problem for a stochastic diffusion equation.
A Hájek-Rényi type inequality and its applications.