Application du calcul stochastique a i'etude de processus de markov reguliers sur [0,1]
- 1 October 1986
- journal article
- research article
- Published by Taylor & Francis in Stochastics
- Vol. 19 (1-2) , 41-82
- https://doi.org/10.1080/17442508608833417
Abstract
In this paper, we will study one-dimensional continuous and regular strong Markov processes on the interval [0,1]. We will show that stochastic calculus methods enable us to obtain a precise description of the behaviour of these processes. We will prove that, up to continuous transformations of the state space, these processes are semimartingales. They all can be obtained from brownian motions reflected at 0 and 1, by time change and killing. Conversely, for any given characteristics, we will explicitly construct a continuous and regular strong Markov process on [0,1] satisfying to them, from a reflected brownian motionKeywords
This publication has 7 references indexed in Scilit:
- Diffusion Processes and their Sample PathsPublished by Springer Nature ,1996
- Instantaneous Control of Brownian MotionMathematics of Operations Research, 1983
- Semimartingales and Markov processesProbability Theory and Related Fields, 1980
- ON CONTINUOUS MARTINGALESProceedings of the National Academy of Sciences, 1965
- Markov ProcessesPublished by Springer Nature ,1965
- The General Diffusion Operator and Positivity Preserving Semi-Groups in One DimensionAnnals of Mathematics, 1954
- Diffusion processes in one dimensionTransactions of the American Mathematical Society, 1954