One can view a 2-parameter Brownian sheet {W (s, t); s, t ≥ 0} as a stream of interacting Brownian motions {W (s, •); s ≥ 0}. Given this viewpoint, we aim to continue the analysis of Walsh (1978) on the local times of the stream W (s, •), near time s = 0. Our main result is a kind of maximal inequality that, in particular, verifies the following conjecture of Khoshnevisan (1995a): as s → 0, the...

Abstract: One can view a 2-parameter Brownian sheet {W (s, t); s, t ≥ 0} as a stream of interacting Brownian motions {W (s, •); s ≥ 0}. Given this viewpoint, we aim to continue the analysis of [20] on the local times of the stream W (s, •) near time s = 0. Our main result is a kind of maximal inequality that, in particular, verifies the following conjecture of [10]: As s → 0, the local times of...

using the mean-value theorem for integrals we tried to solved the nonlinear integral equations of hammerstein type . the mean approach is to obtain an initial guess with unknown coefficients for unknown function y(x). the procedure of this method is so fast and don't need high cpu and complicated programming. the advantages of this method are that we can applied for those integral equation...

in this article, we develop the distributed order fractional hybrid differential equations (dofhdes) with linear perturbations involving the fractional riemann-liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-lipschit...

In this paper, we considered the half logistic model and derived a probability density function that generalized it. The cumulative distribution function, the $n^{th}$ moment, the median, the mode and the 100$k$-percentage points of the generalized distribution were established. Estimation of the parameters of the distribution through maximum likelihood method was accomplished with the aid of c...