We provide cubature formulas for the calculation of derivatives of expected values in the spririt of Terry Lyons and Nicolas Victoir. In financial mathematics derivatives of option prices with respect to initial values, so called Greeks, are of particular importance as hedging parameters. The proof of existence of Cubature formulas for Greeks is based on an argument, which leads to the calculat...

We consider a rational system of first-order difference equations in the plane with four parameters such that all fractions have a common denominator. We study, for the different values of the parameters, the global and local properties of the system. In particular, we discuss the boundedness and the asymptotic behavior of the solutions, the existence of periodic solutions, and the stability of...

We consider a stochastic predator prey model with the Bedington -DeAngelis functional response. Firstly, we prove the existence, uniqueness and positivity of solutions. Then, the boundedness of moments of population are studied. Finally, we show the weak convergence of densities of prey to a singular measure in a special case, and give some upper growth and exponential death rates of population...

We find some new results regarding the existence, uniqueness, boundedness, stability and attractivity of the solutions of a class of initialboundary-value problems characterized by a quasi-linear third order equation which may have non-autonomous forcing terms. The class includes equations arising in superconductor theory, quantum mechanics and in the theory of viscoelastic materials.

We consider a class of stochastic partial differential equations arising as a model for amorphous thin film growth. Using a spectral Galerkin method, we verify the existence of stationary mild solutions, although the specific nature of the nonlinearity prevents us from showing the uniqueness of the solutions as well as their boundedness (in time).

A class of Cohen-Grossberg neural networks with distributed delays are considered. By using the coincidence degree theorem and differential inequality techniques, sufficient conditions for the existence and exponential stability of the periodic solutions are established, Without assuming the boundedness, monotonicity, and differentiability of activation functions and any symmetry of interconnec...

Extension results, expressed in terms of complete boundedness, leading to necessary and sufficient conditions for the solvability of power moment problems with unbounded operator data are given. As an application, necessary and sufficient conditions for the existence of selfadjoint and normal extensions for some classes of commuting tuples of unbounded linear operators are obtained.

A 3D slip-dependent frictional contact problem in elastostatics is discussed. We deliver a variational formulation as a mixed variational problem whose Lagrange multipliers set is solutiondependent. Then, the existence and the boundedness of the solutions is investigated. The proof is based on a recent result for an abstract mixed variational problem with solution-dependent set of Lagrange mult...

In this paper, we investigate the asymptotic dynamics of Fisher-KPP equations with nonlocal dispersal operator and reaction term in time periodic space heterogeneous media. We first show global existence boundedness nonnegative solutions. Next, obtain some sufficient conditions ensuring uniform persistence. Finally, study existence, uniqueness stability positive sol...