Wyniki wyszukiwania - BazTech

Ograniczanie wyników

2 Probability and Mathematical Statistics

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Stochastic volatility : approximation and goodness-of-fit test

Gradinaru M., Nourdin I.

Probability and Mathematical Statistics

2008

Vol. 28, Fasc. 1

1--19

Let X be the unique solution started from x0 of the stochastic differential equation dXt= θ(t;Xt)dBt +b(t;Xt)dt with B a standard Brownian motion. We consider an approximation of the volatility θ(t;Xt), the drift being considered as a nuisance parameter. The approximation is based on a discrete time observation of X and we study its rate of convergence as a process. A goodness-of-fit test is also constructed.

Sojourn time of some reflected Brownian motion in the unit disk

Deaconu M., Gradinaru M., Roche J. R.

Probability and Mathematical Statistics

2000

Vol. 20, Fasc. 1

19--38

We study the heat diffusion in a domain with an obstacle inside. More precisely, we are interested in the quantity of heat in so far as a function of the position of the heat source at time 0. This quantity is also equal to the expectation of the sojourn time of the Brownian motion, reflected on the boundary of a small disk contained in the unit disk, and killed on the unit circle. We give the explicit expression of this expectation. This allows us to make some numerical estimates and thus to illustrate the behaviour of this expectation as a function of starting point of the Brownian motion.