Mathematics
http://hdl.handle.net/2022/13431
Thu, 18 Oct 2018 12:01:47 GMT2018-10-18T12:01:47ZStrong solutions of stochastic differential equations for multiparameter processes
http://hdl.handle.net/2022/22275
Strong solutions of stochastic differential equations for multiparameter processes
Puri, Madan L.; Dozzi, Markus
We consider the stochastic differential equation (SDE) $X_t = V_t \int_{[0,t]}f(s,\omega, X.(\omega)),dZ_5(\omega)$, where $V$ and $Z$ are vector valued process indexed by $t\varepsilon\Re^p_+$. The assumptions we make on $Z$ and on the increasing process controlling $Z$ are satisfied by certain classes of square integrable martingales, by processes of finite variation and by mixtures of these types of processes. Existence, uniqueness and the possibility of explosions of a strong solution $X$ are investigated under Lipschitz conditions on $f$. A well-known sufficient condition for non-explosion is shown to work also in the multiparameter case and stability of $X$ under perturbation of $V$, $f$ and $Z$ is proved. Finally more special SDE without Lipschitz conditions are considered, including a class of SDE of the Tsirel'son type.
A freely accessible, full text version is available using the link(s) in "Other versions".
Wed, 01 Jan 1986 00:00:00 GMThttp://hdl.handle.net/2022/222751986-01-01T00:00:00ZA multivariate Wald‐Wolfowitz rank test against serial dependence
http://hdl.handle.net/2022/22265
A multivariate Wald‐Wolfowitz rank test against serial dependence
Puri, Madan L.; Hallin, Marc
Rank‐based cross‐covariance matrices, extending to the case of multivariate observed series the (univariate) rank autocorrelation coefficients introduced by Wald and Wolfowitz (1943), are considered. A permutational central limit theorem is established for the joint distribution of such matrices, under the null hypothesis of (multivariate) randomness as well as under contiguous alternatives of (multivariate) ARMA dependence. A rank‐based, permutationaily distribution‐free test of the portmanteau type is derived, and its asymptotic local power is investigated. Finally, a modified rank‐based version of Tiao and Box's model specification procedure is proposed, which is likely to be more reliable under non‐Gaussian conditions, and more robust against gross errors.
Publisher's, offprint version
Wed, 01 Mar 1995 00:00:00 GMThttp://hdl.handle.net/2022/222651995-03-01T00:00:00ZAsymptotic normality of the lengths of a class of nonparametric confidence intervals for a regression parameter
http://hdl.handle.net/2022/22264
Asymptotic normality of the lengths of a class of nonparametric confidence intervals for a regression parameter
Puri, Madan L.; Wu, Tiee‐Jian
In the linear regression model, the asymptotic distributions of certain functions of confidence bounds of a class of confidence intervals for the regression parameter arc investigated. The class of confidence intervals we consider in this paper are based on the usual linear rank statistics (signed as well as unsigned). Under suitable assumptions, if the confidence intervals are based on the signed linear rank statistics, it is established that the lengths, properly normalized, of the confidence intervals converge in law to the standard normal distributions; if the confidence intervals arc based on the unsigned linear rank statistics, it is then proved that a linear function of the confidence bounds converges in law to a normal distribution.
Publisher's, offprint version
Sat, 01 Sep 1984 00:00:00 GMThttp://hdl.handle.net/2022/222641984-09-01T00:00:00ZAsymptotic Normality of Nearest Neighbor Regression Function Estimates Based on Nonstationary Dependent Observations
http://hdl.handle.net/2022/22263
Asymptotic Normality of Nearest Neighbor Regression Function Estimates Based on Nonstationary Dependent Observations
Harel, Michel; Puri, Madan L.
In this paper the convergence of the regression function estimators and the central limit theorem for these estimators are proved for the case when the underlying sequence of random variables is dependent and nonstationary.
Offprint, publisher's version
Sun, 01 Jan 1995 00:00:00 GMThttp://hdl.handle.net/2022/222631995-01-01T00:00:00Z