This letter derives some new exponential bounds for discrete time, real valued, conditionally symmetric martingales with bounded jumps. The new bounds are extended to conditionally symmetric sub/ supermartingales, and are compared to some existing bounds.

Let Hn(z) be the function of a complex variable z defined by

We derive Wiman’s asymptotic formula for the number of generalized zeros of (nontrivial) solutions of a second order dynamic equation on a time scale. The proof is based on the asymptotic representation of solutions via exponential functions on a time scale. By using the Jeffreys et al. approximation we prove Wiman’s formula for a dynamic equation on a time scale. Further we show that using the...

We recently formulated a model of the universe based on an underlying W3symmetry. It allows the creation of the universe from nothing and the creation of baby universes and wormholes for spacetimes of dimension 2, 3, 4, 6 and 10. Here we show that the classical large time and large space limit of these universes is one of exponential fast expansion without the need of a cosmological constant. U...

One of the basic problems for Lie groups is to describe the image of the exponential map. A Lie group H is called exponential resp. weakly exponential if its exponential map is surjective resp. has dense image in H . In this paper we classify all exponential groups which are identity components of almost simple real algebraic groups. The weakly exponential groups of this type were determined in...

We survey some important properties of fields of generalized series and of exponential-logarithmic series, with particular emphasis on their possible differential structure, based on a joint work of the author with S. Kuhlmann [KM12b, KM11].

It is well known [4] that the non-Archimedean residue class fields K of the ring of continuous real valued functions on a space are realclosed and 7/i-sets. It does not appear to be known that the exponential function in the reals induces an exponential function in K (definitions to follow) ; thus K is exponentially closed. The property of being exponentially closed is a new invariant which wil...

Large deviation principles are proved for rescaled Poisson random measures. As a consequence, FreidlinWentzell type large deviations results for processes with independent increments are obtained in situations where exponential moments are infinite.

Computable expressions are obtained for the nonning constants for certain exponential distributional models on the sphere. The method used evaluates the nonning constant for any member of the general exponential family treated by Beran (Arm. Statist., '!.. (1979), 1162-1178), and we illustrate by providing explicit results in the case of the 8-parameter Fisher-Bingham distribution considered by...