Hyperbolic equations arising in random models

Ci{models Arising among 4 Random Variables

Orbit Spaces Arising from Isometric Actions on Hyperbolic Spaces

Let be a differentiable action of a Lie group on a differentiable manifold and consider the orbit space with the quotient topology.  Dimension of is called the cohomogeneity of the action of  on . If is a differentiable manifold  of  cohomogeneity one under the action of  a compact and connected Lie group, then the orbit space is homeomorphic to one of the spaces , , or . In this paper we suppo...

Stochastic Optimal Control of Delay Equations Arising in Advertising Models

We consider a class of optimal control problems of stochastic delay differential equations (SDDE) that arise in connection with optimal advertising under uncertainty for the introduction of a new product to the market, generalizing classical work of Nerlove and Arrow [30]. In particular, we deal with controlled SDDE where the delay enters both the state and the control. Following ideas of Vinte...

Numerical Study of Hyperbolic Equations with Integral Constraints Arising in Semiconductor Theory

An efficient numerical scheme is described for the solution of certain types of nonlinear hyperbolic equations with an integral constraint which are used to model the Gunn effect in semiconductors with impurity capture. We analyze the stability and convergence properties of the scheme and present the results of numerical simulations. Depending on the value of the parameters defining the problem...

Random fractional functional differential equations

In this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the Lipschitz type condition. Moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.