UNIVERSITY
OF WROCŁAW
 
Main Page
Contents
Online First
General Information
Instructions for authors


VOLUMES
43.2 43.1 42.2 42.1 41.2 41.1 40.2
40.1 39.2 39.1 38.2 38.1 37.2 37.1
36.2 36.1 35.2 35.1 34.2 34.1 33.2
33.1 32.2 32.1 31.2 31.1 30.2 30.1
29.2 29.1 28.2 28.1 27.2 27.1 26.2
26.1 25.2 25.1 24.2 24.1 23.2 23.1
22.2 22.1 21.2 21.1 20.2 20.1 19.2
19.1 18.2 18.1 17.2 17.1 16.2 16.1
15 14.2 14.1 13.2 13.1 12.2 12.1
11.2 11.1 10.2 10.1 9.2 9.1 8
7.2 7.1 6.2 6.1 5.2 5.1 4.2
4.1 3.2 3.1 2.2 2.1 1.2 1.1
 
 
WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 20, Fasc. 2,
pages 343 - 358
 

EXISTENCE AND NON-EXISTENCE OF SOLUTIONS OF ONE-DIMENSIONAL STOCHASTIC EQUATIONS

H. J. Engelbert

Abstract: We consider the one-dimensional stochastic equation

integral t integral t Xt = x0 + b(Xs)d<M >s + s(Xs)dMs 0 0
for a continuous local martingale M with square variation <M > and measurable drift and diffusion coefficients b and s. The main purpose of this paper is to derive a necessary condition for the existence of a solution X starting from x0. As a result, we construct a diffusion coefficient s such that the above stochastic equation has no solution X whatever the initial value x0 and the non-zero, say, continuous drift coefficient b might be.

1991 AMS Mathematics Subject Classification: 60H10, 60G44.

Key words and phrases: Stochastic equations, continuous local martingales, non-existence, local time.

Download:    Abstract    Full text   Abstract + References