Abstract
AbstractA partially observed jump diffusion $$Z=(X_t,Y_t)_{t\in [0,T]}$$
Z
=
(
X
t
,
Y
t
)
t
∈
[
0
,
T
]
given by a stochastic differential equation driven by Wiener processes and Poisson martingale measures is considered when the coefficients of the equation satisfy appropriate Lipschitz and growth conditions. Under general conditions it is shown that the conditional density of the unobserved component $$X_t$$
X
t
given the observations $$(Y_s)_{s\in [0,t]}$$
(
Y
s
)
s
∈
[
0
,
t
]
exists and belongs to $$L_p$$
L
p
if the conditional density of $$X_0$$
X
0
given $$Y_0$$
Y
0
exists and belongs to $$L_p$$
L
p
.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Modeling and Simulation,Statistics and Probability
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