Keywords
associated counting processes
fixed points
canonical aditive descomposition
L2- regulares martingales in quasi-intervals
regularity conditions of trajectories
total variation
nearby processes
procesos de incrementos independientes en casi intervalos
procesos de conteo asociados
puntos fijos
descomposición aditiva canónica
martingalas L2- regulares en casi intervalos
condiciones de regularidad de las trayectorias
variación total
nearby processes
How to Cite
Abstract
We introduce the notion independent increment in quasi-intervals. Some properties of the fixed points of these processes are studied, as well as those of the aditive descomposition. Finally, we establish the relation between this concept with the classical one and we deduce a property of the total variation of continuous-time processes.
References
Nelson, E. (1977) “Internal Set Theory: a new approach to nonstandar analysis ”, Bulletin of the American Mathematical Society 83(6).
Nelson, E. (1987) Radically Elementary Probability Theory. Princeton University Pres.
Stroyan, B. (1986) Foundations of Infinitesimal Stochastic Analysis. North Holland, Amsterdam.
Lobo, J. (1995) “Estudio en tiempo discreto de los procesos puntuales de incrementos condicionalmente independientes”, Revista de Matemática: Teoría y Aplicaciones 2(2): 9–16.
Lobo, J. (1995) “Una noción de proceso puntual en tiempo discreto”, Revista de Matemática: Teoría y Aplicaciones 2(1): 17–25.
Lobo, J. (1985) Processus Accroissements Indépendants et Méthode des Semimartingales. Tesis de Doctorado de 3er. ciclo, Universidad de Paris 6.
Lindstrom (1986) “Nonstandar constructions of diffusions and related processes”, Memorias del 1er. Congreso Mundial de la Sociedad Bernoulli, Vol. 1, Scientific Press.
Albeverio (1986) Nonstandar Methods in Stochastic Analysis and Mathematical Physics. Academic Press, New York.
Chuaquí, R. (1991)Truth, Possibility and Probability. North Holland, Amsterdam.