-variation for families of local times on lines
Se introduce una estructura de vorticidad basada en el movimiento browniano fraccionario con parámetro de Hurst H > 1/2 . El objeto de esta nota es presentar el siguiente resultado: Bajo una condición de integrabilidad adecuada sobre la medida ρ que controla la concentración de la vorticidad a lo largo de los filamentos, la energía cinética de la configuración está bien definida y tiene momentos de todos los órdenes.
A model of vortex filaments based on stochastic processes is presented. In contrast to previous models based on semimartingales, here processes with fractal properties between and are used, which include fractional Brownian motion and similar non-Gaussian examples. Stochastic integration for these processes is employed to give a meaning to the kinetic energy.
The paper is devoted to properties of generalized set-valued stochastic integrals defined in [10]. These integrals generalize set-valued stochastic integrals defined by E.J. Jung and J.H. Kim in the paper [4]. Up to now we were not able to construct any example of set-valued stochastic processes, different on a singleton, having integrably bounded set-valued integrals defined in [4]. It was shown by M. Michta (see [11]) that in the general case set-valued stochastic integrals defined by E.J. Jung...
We introduce set-valued stochastic integrals driven by a square-integrable martingale and by a semimartingale. We investigate properties of both integrals.