Abstract We study the Volterra integro-differential equation on time scales and provide sufficient conditions for boundness of all solutions considered equation. Using that result, we present exponential stability All results proved general scale include both integral discrete equations.

The replicator equation is interpreted as a continuous inference equation and a formal similarity between the discrete replicator equation and Bayesian inference is described. Further connections between inference and the replicator equation are given including a discussion of information divergences, evolutionary stability, and exponential families as solutions for the replicator dynamic, usin...

The availability of intraday stock/index return in the web facilitates the improvement of return volatility estimation over the traditional method that is based on inter-day return data. Truncated Levy process distribution is used to extract the intraday return distribution parameters. The calibration to the volatility for Black-Scholes option pricing is studied using the data from Levy-Gaussia...

The complexity of computing the Galois group of a linear differential equation is of general interest. In a recent work, Feng gave the first degree bound on Hrushovski’s algorithm for computing the Galois group of a linear differential equation. This bound is the degree bound of the polynomials used in the first step of the algorithm for finding a proto-Galois group (see Definition 2.8) and is ...

In this article we consider the Levy processes and the corresponding semi-group. We represent the generator of this semigroup in a convolution form. Using the obtained convolution form and the theory of integral equations we investigate the properties of a wide class of Levy processes (potential, quasi-potential, the probability of the Levy process remaining within the given domain, long time b...