A nearly unstable sequence of stationary spatial autoregressive processes is investigated, when the sum of the absolute values of the autoregressive coefficients tends to one. It is shown that after an appropriate normalization the least squares estimator for these coefficients has a normal...

Let <InlineEquation ID="Equ1"> <EquationSource Format="TEX"><![CDATA[$\{X_j\}^\infty_0$]]></EquationSource> </InlineEquation> be a Markov chain with a unique stationary distribution <InlineEquation ID="Equ2"> <EquationSource Format="TEX"><![CDATA[$\pi$]]></EquationSource> </InlineEquation>. Let h be a bounded measurable function. Write <InlineEquation ID="Equ3"> <EquationSource Format="TEX"><![CDATA[$\lambda_{h}=\int hd\pi$]]></EquationSource> </InlineEquation> and <InlineEquation ID="Equ4"> <EquationSource Format="TEX"><![CDATA[$\hat{\lambda}_{hn}=\frac{1}{(n+1)}\sum^n_0h(X_j)$]] ></EquationSource> </InlineEquation>. This paper explores conditions for the <InlineEquation ID="Equ5"> <EquationSource Format="TEX"><![CDATA[$\sqrt{n}$]]></EquationSource> </InlineEquation> consistency and asymptotic normality of the estimate of <InlineEquation ID="Equ6"> <EquationSource Format="TEX"><![CDATA[$\hat{\lambda}_{hn}$]]></EquationSource> </InlineEquation> of <InlineEquation ID="Equ7"> <EquationSource Format="TEX"><![CDATA[$\lambda_h$]]></EquationSource> </InlineEquation> assuming the existence of a solution to the Poisson equation <InlineEquation ID="Equ8"> <EquationSource Format="TEX"><![CDATA[$h - \lambda_h=g-Pg$]]></EquationSource> </InlineEquation>....</equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation>

A parameterized family of financial market models is presented. These models have jumps intrinsic to the price processes yet have strict completeness, equivalent martingale measures, and no arbitrage. For each value of the parameter $\beta (-2\leq\beta 0)$ the model is just as rich as the...

Estimation of ([alpha], [beta])' in the doubly geometric model Zij = [alpha]Zi - 1, j + [beta]Zi, j - 1 - [alpha][beta]Zi - 1, j - 1 + [var epsilon] cases (i) [alpha] = 1,|[beta]| 1 and (ii) [alpha] = [beta] = 1. In each case, the "one step Gauss-Newton estimator" is shown, when properly...

Consider a p-variate counting process N = (...) with jump times {...}. Suppose that the intensity of jumps ... of ... at time t depends on the other components, i. e. ..., where the ... are unknown, nonrandom functions. From observing one single trajectory of the processes N over an increasing...