A 22-year-old Checotaw, Oklahoma, man was killed Monday morning in a single vehicle accident near Guion in Izard County.
According to a preliminary fatal crash summary from the Arkansas State Police, Cody L. Killingsworth was killed in the accident on State Highway 58.
The report says a 2013 John Deere was stalled on the highway, blocking both lanes of traffic. Killingsworth was standing on the left side of the vehicle when it suddenly began traveling north and struck him. The vehicle then exited the highway and came to rest in a wooded area.
The weather was rainy and road conditions wet at the time of the 9:25 a.m. accident.
WebReadyTM Powered by WireReady® NSIHi I am using CoreData to populate a list of products. I want the list to be sorted by "make" + then "model". Seems simple but for some reason the list does not get sorted. Any Ideas What The Issue Is??
My List Is...
Could you give an example what do you get and what do you expect? Are the data types in make and model correct?
Hi make + model are both Strings.
Instead I just get a random order.Baked sweet curd served chilled. Recipe courtesy - chef Murli Gupta.
Take 1/2 cup hung curd, 1 cup milk powder, and half cup fresh cream.
In a mixing bowl add curd and milk powder.
Add fresh cream to curd mixture and mix well.
Pour this mixture into oven proof bowls or moulds. Fill 2/3rd as it will rise little while baking though set down after removing from oven.
Heat a cooker for five minutes.
Don't forget to remove the whistle.
Take an oven proof tray and fill with 1 cup water.
Put a stand in cooker.
Place water filled tray over stand in cooker.
Place curd mixture bowls in tray.
Cover the lid of cooker without whistle and put the flame on medium.
Remove the tray from cooker and let it cool down.
Place the baked curd moulds in refrigerator to chill for 4 to 6 hours.
When chilled serve as it is topped with nuts and fruits, or demould first and then serve.\section{Introduction} \label{sec1}
\setcounter{equation}{0}
\renewcommand{\theequation}{\thesection.\arabic{equation}}

Local times are fundamental objects in the theory of stochastic processes. The local time of the process $X$ at time $t$ and level $x$ essentially measures the time spent by the process at point $x$ between time $0$ and time $t$. More precisely, let $X=(X_t)_{t \geq 0}$ be defined on a filtered probability space $(\Omega, \mathcal{F}, 
(\mathcal{F}_t)_{t \geq 0}, \mathbb P)$. Recall that the occupation measure $\nu$ associated with $X$ is defined via
\begin{align} \label{occupation}
\nu_t(A) := \int_0^t 1_{A} (X_s) ds,
\end{align}
for any Borel measurable set $A \subset \R$.  If the measure $\nu_t$ admits a Lebesgue density, we call it the local time of $X$ and denote it by 
\begin{align} \label{ltime}
L_t (x) := \frac{d \nu_t}{dx} (x).
\end{align}
An immediate consequence of the existence of local times is the occupation times formula, which states the identity 
\begin{align} \label{otf}
\int_0^t f(X_s) ds = \int_{\R} f(x) L_t (x) dx
\end{align}
with $f$ being a Borel function on $\R$.\\

The theory of occupation measures and local times has been intensively studied in the literature for several decades. A general criterion for existence of local times is provided in \cite{GH}. Properties of the local time of a Brownian motion, or more generally of a continuous diffusion process, have been particularly investigated. We refer to the monograph \cite{RY} for a comprehensive study.  In \cite{B} the author focuses on sample paths properties in the case of stationary Gaussian processes.\\ 
 
Then a natural question is that of the estimation of local times based on discrete high frequency observations of the process $X$ over $[0,t]$: $X_0, X_{1/n}, X_{2/n}, \ldots, X_{[nt]/n}$, where the asymptotic setting is that $n$ goes to infinity. From \eqref{ltime}, a natural estimator of $L_t (x)$ is given by the statistic
\[
\frac{u_n}{n}\sum_{i=1}^{[nt]} 1_{\left\{|X_{i/n}-x| \leq 1/u_n \right\}},
\]
where $u_n$ is a sequence of positive real numbers with $u_n \to \infty$. In general we may consider a larger class of statistics, which have the form 
\begin{align} \label{Vg}
V(g)_t^n:= \frac{u_n}{n}\sum_{i=1}^{[nt]} g\left(u_n (X_{i/n}-x)\right) \qquad \text{with} \qquad g \in L^1(\R). 
\end{align}  
Indeed, the statistic $V(g)_t^n$ is, up to a constant, a good estimator of $L_t(x)$. This can be seen from the following intuitive argument, which follows from the occupation time formula:
\begin{align*}
V(g)_t^n &\approx u_n \int_0^t g(u_n (X_s-x)) ds = u_n \int_{\R} g(u_n (y-x)) L_t (y) dy \\[1.5 ex]
&=  \int_{\R} g(z) L_t (x+z/u_n) dz \toop L_t(x)  \int_{\R} g(z) dz,
\end{align*} 
where the last convergence follows from the continuity of the local time in space.  Despite this simple intuition, the first approximation in the above argument is not trivial to prove (in particular it is wrong if 
$u_n /n \to \infty$). Such convergence results have been shown in the framework of Brownian motion in 
\cite{B86, B89} and they were extended in \cite{J98} to the setting of continuous diffusion processes (in the latter article the author has also shown the associated central limit theorems). In \cite[Theorem 4]{J04} the consistency of $V(g)_t^n$ has been proved for linear fractional stable motions.\\   

In \cite{J98}, with the purpose of statistical applications, a more general class of functionals than $V(g)_t^n$ is actually considered in the setting of continuous diffusion processes. More specifically, for a measurable function $f: \R^2 \to \R$ satisfying certain conditions to be specified below, the author studies statistics of the form
\begin{align} \label{Vf}
V(f)_t^n:= \frac{u_n}{n}\sum_{i=0}^{[nt]} f \left(u_n (X_{i/n}-x), u_n \Delta_i^n X \right) \qquad \text{where} \qquad 
\Delta_i^n X = X_{(i+1)/n} - X_{i/n}.
\end{align} 

In this work, we wish to somehow extend the approaches in \cite{J98} and \cite{J04}. Indeed we want to investigate the behavior of $V(f)_t^n$ in the case where the underlying process $X$ satisfies 
\begin{align} \label{fbm}
X_t = \sigma B_t^H,
\end{align} 
where $\sigma>0$ is a scale parameter and $(B_t^H)_{t \geq 0}$ is a standard fractional Brownian motion with Hurst parameter $H \in (0,1)$, that is a zero mean Gaussian process with covariance kernel given by
\[
\E[B_t^H B_s^H]= \frac{1}{2} \left(t^{2H} + s^{2H} -|t-s|^{2H} \right).
\] 
The fractional Brownian motion has stationary increments and it is self-similar with parameter $H$: $(B_{at}^H)_{t \geq 0} \eqschw (a^HB_{t}^H)_{t \geq 0}$ for any $a>0$. Furthermore, local times of $B^H$ exist for any $H \in (0,1)$ and are known to be continuous in time and space, see \cite{B2}.\\

Studying high frequency statistics in the