10 research outputs found
A new class of stochastic processes with great potential for interesting applications
This paper contributes to the study of a new and remarkable family of
stochastic processes that we will term class . This class is
potentially interesting because it unifies the study of two known classes: the
class and the class . In other words, we consider
the stochastic processes which decompose as , where is a local
martingale, and are finite variation processes such that is
carried by and the support of is , the set of
zeros of some continuous martingale . First, we introduce a general
framework. Thus, we provide some examples of elements of the new class and
present some properties. Second, we provide a series of characterization
results. Afterwards, we derive some representation results which permit to
recover a process of the class from its final value and of the
honest times and . In final, we
investigate an interesting application with processes presently studied. More
precisely, we construct solutions for skew Brownian motion equations using
stochastic processes of the class .Comment: 23 page