Bruce Lavoie wrote:
>
> Thanks for the quick reply, I have attached a few lines of my file. It
> seems sometimes (not all the time) when I open the file I need to fix the
> formatting of the integrals etc...
from my point of view this problem belongs to your boldmath. you used
{\bf x}. this is only the
latex command for bold in textmode. in textmode it's not possible to use
the integrallimits like in
mathmode. in textmode there is only super/subscript. look for the first
formula in the textline,
which i inserted (they make no sense .. ;-). there were other formulas
inserted too. look for this,
if the lime are correct.
bold font in mathmode is \mathbf{x} or better with the key ctrl-b (bold
on/off), it works
right in textmode (\bf) and in mathmode (\mathbf{}).
Herbert
p.s. by the way ...
your last formula "moments" with the double integral has for the first
int the same limits.
is this right?
--
[EMAIL PROTECTED]
http://perce.de/voss
#LyX 1.1 created this file. For more info see http://www.lyx.org/
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\spacing other 1.30
\papersize Default
\paperpackage a4
\use_geometry 0
\use_amsmath 0
\paperorientation portrait
\secnumdepth 3
\tocdepth 3
\paragraph_separation indent
\defskip bigskip
\quotes_language english
\quotes_times 2
\papercolumns 1
\papersides 1
\paperpagestyle default
\layout Standard
The pdf acts as a weighting function, the probability of an experimental
outcome being between two bounds
\begin_inset Formula \( [\eta _{1},\eta _{2}] \)
\end_inset
can then be found
\begin_inset Formula \( p_{s}(\eta _{1}<s<\eta _{2})=\int ^{\eta _{2}}_{\eta
_{1}}f_{\mathbf{x}}(x,t)dx \)
\end_inset
as
\begin_inset Formula \begin{equation}
\label{probability of n1 < s < n2}
p_{s}(\eta _{1}<s<\eta _{2})=\int ^{\eta _{2}}_{\eta _{1}}f_{\mathbf{x}}(x,t)dx
\end{equation}
\end_inset
\layout Standard
\begin_inset Formula \[
p_{s}(\eta _{1}<s<\eta _{2})=\int _{\eta _{1}}^{\eta _{2}}f_{\mathbf{x}}(x,t)dx\]
\end_inset
\layout Standard
\begin_inset Formula \begin{eqnarray*}
p_{s} & = & \int _{a}^{b}f(x)dx\\
w & = & \sum _{i=3}^{14}ki^{2}=k\int _{a}^{b}g(y)dy
\end{eqnarray*}
\end_inset
Because this research will ultimately be concerned with the relationship
between two stochastic processes, there must be some mechanism to relate
one process to the other.
This is where the
\emph on
Second-Order
\emph default
statistics are needed.
The
\emph on
joint
\emph default
pdf
\begin_inset Formula \( f_{\mathbf{xy}}(x_{1},y_{2};t_{1},t_{2}) \)
\end_inset
is used to describe the statistical properties between the two stochastic
processes
\begin_inset Formula \( \mathbf{x}(t,S) \)
\end_inset
and
\begin_inset Formula \( \mathbf{y}(t,S) \)
\end_inset
is defined as
\begin_inset Formula \begin{equation}
f_{\mathbf{xy}}(x_{1},y_{2};t_{1},t_{2})=\frac{\partial
^{2}F_{\mathbf{xy}}(x_{1},y_{2};t_{1},t_{2})}{\partial x_{1}\partial y_{2}}
\end{equation}
\end_inset
The relationship between the two processes is then quantified using the
joint moments of the two processes as follows
\begin_inset Formula \begin{equation}
\label{moments}
E\{\mathbf{x}^{i}(t_{1})\mathbf{y}^{j}(t_{2})\}=\int _{+\infty }^{+\infty }\int
_{-\infty }^{+\infty
}x^{i}_{1}y_{2}^{j}f_{\mathbf{xy}}(x_{1},y_{2};t_{1},t_{2})dx_{1}dy_{2}
\end{equation}
\end_inset
\layout Standard
\begin_inset Formula \[
E\{\mathbf{x}^{i}(t_{1})\mathbf{y}^{j}(t_{2})\}=\int _{+\infty }^{+\infty }\int
_{-\infty }^{+\infty
}x^{i}_{1}y_{2}^{j}f_{\mathbf{xy}}(x_{1},y_{2};t_{1},t_{2})dx_{1}dy_{2}\]
\end_inset
If the process is at least Wide-Sense Stationary (WSS)
\begin_inset LatexCommand \cite{papoulis}
\end_inset
, which is assumed in this work,
\the_end
