We obtain general weak existence and stability results for stochastic convolution equations with jumps under mild regularity assumptions, allowing non-Lipschitz coefficients singular kernels. Our approach relies on convergence in Lp spaces. The main tools are new a priori estimates Sobolev–Slobodeckij norms of the solution, as well novel martingale problem that is equivalent to original equatio...

We consider a size-structured population model where individuals may be recruited into the population at different sizes. First- and second-order finite difference schemes are developed to approximate the solution of the model. The convergence of the approximations to a unique weak solution is proved. We then show that as the distribution of the new recruits become concentrated at the smallest ...

In this paper, we study a generalization of z-ideals in the ring C(X) of continuous real valued functions on a completely regular Hausdorff space X. The notion of a weak ideal and naturally a weak z-ideal and a prime weak ideal are introduced and it turns out that they behave such as z-ideals in C(X).

Non-statistical weak measurements yield weak values that are outside the range of eigenvalues and are not rare, suggesting that weak values are a property of every preand-post-selected ensemble. They also extend the applicability and valid regime of weak values.

In this paper, we will establish some xed point results for two pairs of self mappings satisfying generalized contractive condition by using a new concept as weak subsequential continuity with compatibility of type (E) in metric spaces, as an application the existence of unique common solution for a system of functional equations arising in system programming is proved.

In this paper we consider the European continuous installment call option. Then  its linear complementarity formulation is given. Writing the resulted problem in variational form, we prove the existence and uniqueness of its weak solution. Finally finite element method is applied to price the European continuous installment call option.