An ergodic-type theorem for generalized Ornstein–Uhlenbeck processes
-
Andriy Yurachkivsky
Abstract.
Let 
be an ℝd-valued càdlàg random process, and let
F be an increasing from zero ℝ-valued random process whose
values at all times are measurable w.r.t. some σ-algebra
(the class of all such processes is denoted by
). Conditions guaranteing that for every bounded continuous
function 
are found. In the most general theorem they are formulated in
terms of F and . Further we consider the case when
satisfies an equation of the kind
where 
is an 
-measurable random variable, 
is a continuous
process of class , A is a matrix-valued random process
-measurable in 
, and S is an
ℝd-valued semimartingale with conditionally on
independent increments and initial value 0. In this case,
sufficient conditions for (
) are stated in terms of F and
the constituents of the equation. Besides, the characteristic function
of an n-dimensional distribution of is found.
© 2013 by Walter de Gruyter Berlin Boston
Articles in the same Issue
- Masthead
- An ergodic-type theorem for generalized Ornstein–Uhlenbeck processes
- A note on Feynman–Kac path integral representations for scalar wave motions
- Mutual information for stochastic differential equation with subfractional noises
- The quasi maximum likelihood approach to statistical inference on a nonstationary multivariate ARFIMA process
Articles in the same Issue
- Masthead
- An ergodic-type theorem for generalized Ornstein–Uhlenbeck processes
- A note on Feynman–Kac path integral representations for scalar wave motions
- Mutual information for stochastic differential equation with subfractional noises
- The quasi maximum likelihood approach to statistical inference on a nonstationary multivariate ARFIMA process
