and Applied Analysis 3 when ω 1 and δ 0, 1.4 reduces to the probability of ruin ψi u P T < ∞ | J 0 i,U 0 u , u ≥ 0. 1.6 The purpose of this paper is to present some numerical results on the GerberShiu function for the Markov-modulated diffusion risk model with arbitrary upward and downward jumps. In Section 2 we derive a system of integrodifferential equations and approximate solutions for φi u...

An abstract integrodifferential equation arising from linear viscoelasticity is considered. The stability properties of the related C0-semigroup are discussed, in dependence on the form of the convolution (memory) kernel.

We develop a quasilinear theory of the 2D Euler equation and derive an integrodifferential equation for the evolution of the coarse-grained vorticity omega;(r,t). This equation respects all of the invariance properties of the Euler equation and conserves angular momentum in a circular domain and linear impulse in a channel. We show under which hypothesis we can derive an H theorem for the Fermi...

The question is studied whether weak solutions of linear partial integrodifferential equations approach a constant spatial profile after rescaling, as time goes to infinity. The possible limits and corresponding scaling functions are identified and are shown to actually occur. The limiting equations are fractional diffusion equations which are known to have self-similar fundamental solutions. F...