Affiliation:
1. National School of Applied Sciences Agadir Morocco , Ibn Zohr University , Agadir , Morocco ; and Department of Industrial Engineering, System Engineering and Decision Support Laboratory (LISAD)
2. Departement of Mathematics , Faculty of Sciences , Mohamed First University , Oujda , Morocco ; and Stochastic and Deterministic Modelling Laboratory (LAMSD)
Abstract
Abstract
The generalized Brownian bridge
X
a
,
b
,
T
{X^{a,b,T}}
from a to b of length T was used in several fields such as in mathematical finance, biology and statistics. In this paper, we study the following stochastic properties and characteristics of this process: The Hölder continuity, the self-similarity, the quadratic variation, the Markov property, the stationarity of the increments,
and the α-differentiability of the trajectories.
Subject
Statistics and Probability,Analysis
Reference21 articles.
1. L. Bachelier,
Théorie de la spéculation,
Ann. Sci. Éc. Norm. Supér. (3) 17 (1900), 21–86.
2. F. Ben Adda and J. Cresson,
About non-differentiable functions,
J. Math. Anal. Appl. 263 (2001), no. 2, 721–737.
3. A. N. Borodin and P. Salminen,
Handbook of Brownian Motion—Facts and Formulae,
Probab. Appl.,
Birkhäuser, Basel, 1996.
4. R. Brown,
A brief account of microscopical observations made in the months of June, July and August 1827, on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies,
Ann. Phys. 14 (1828), 294–313.
5. C. Cheng,
A Brownian bridge movement model to track mobile targets,
Thesis, Naval Postgraduate School, Monterey, 2016.