Stochastic analysis and applications

Stochastic Analysis and Applications

In this paper, we study Dirichlet operators on certain smooth Banach spaces. We establish the well-known Kato's inequality in our general infinite dimensional setting. By applying this,we show the essential self-adjointness of Dirichlet operators with non-constant diffusion part on certain smooth Banach spaces. We also provide an approximation criterion for essential self-adjointness of Dirichl...

Stochastic Analysis and Applications

The world we live in has never been very predictable, and randomness has always been part of our lives. There is ample evidence that our ancestors did enjoy playing games of chance, and the early development of probability theory had to do with these games. The study of probability has always been motivated by potential applications. Besides gambling, the stimulus has come from life insurance, ...

Stochastic Analysis and Applications

In this article, we study the discounted penalty at ruin in a perturbed compound Poisson model with two-sided jumps. We show that it satisfies a renewal equation under suitable conditions and consider an application of this renewal equation to study some perpetual American options. In particular, our renewal equation gives a generalization of the renewal equation in Gerber and Landry [2] where ...

Stochastic Analysis and Applications

A difference approximation that is second-order accurate in the time step h is derived for the general Ito stochastic differential equation. The difference equation has the form of a second-order random walk in which the random terms are non-linear combinations of Gaussian random variables. For a wide class of problems, the transition pdf is joint-normal to second order in h; the technique then...

Stochastic Analysis and Applications