A discrete-time proof of Neveu's exchange formula

1995 ◽  
Vol 32 (4) ◽  
pp. 917-921
Author(s):  
Takis Konstantopoulos ◽  
Michael Zazanis
Keyword(s):  
Stochastic Processes ◽  
Discrete Time ◽  
Point Processes ◽  
Simple Point ◽  
Simple Result ◽  
Stationary Stochastic Processes ◽  
Palm Probabilities

Neveu's exchange formula relates the Palm probabilities with respect to two jointly stationary simple point processes. We give a new proof of the exchange formula by using a simple result from discrete time stationary stochastic processes.

A discrete-time proof of Neveu's exchange formula

1995 ◽  
Vol 32 (04) ◽  
pp. 917-921
Author(s):  
Takis Konstantopoulos ◽  
Michael Zazanis
Keyword(s):  
Stochastic Processes ◽  
Discrete Time ◽  
Point Processes ◽  
Simple Point ◽  
Simple Result ◽  
Stationary Stochastic Processes ◽  
Palm Probabilities

Neveu's exchange formula relates the Palm probabilities with respect to two jointly stationary simple point processes. We give a new proof of the exchange formula by using a simple result from discrete time stationary stochastic processes.

MARTINGALE APPROXIMATION OF NON-STATIONARY STOCHASTIC PROCESSES

2006 ◽  
Vol 06 (02) ◽  
pp. 173-183 ◽  
Author(s):  
DALIBOR VOLNÝ
Keyword(s):  
Large Deviations ◽  
Stochastic Processes ◽  
Discrete Time ◽  
Invariance Principle ◽  
Limit Theorems ◽  
Orlicz Spaces ◽  
Stationary Case ◽  
Martingale Approximation ◽  
Stationary Stochastic Processes ◽  
Log Law

We generalise the martingale-coboundary representation of discrete time stochastic processes to the non-stationary case and to random variables in Orlicz spaces. Related limit theorems (CLT, invariance principle, log–log law, probabilities of large deviations) are studied.

scholarly journals Linear rigidity of stationary stochastic processes

2017 ◽  
Vol 38 (7) ◽  
pp. 2493-2507 ◽  
Author(s):  
ALEXANDER I. BUFETOV ◽  
YOANN DABROWSKI ◽  
YANQI QIU
Keyword(s):  
Stochastic Processes ◽  
Point Processes ◽  
Linear Span ◽  
Sufficient Condition ◽  
Determinantal Point Processes ◽  
Determinantal Point Process ◽  
Zygmund Class ◽  
Closed Linear Span ◽  
Stationary Stochastic Processes ◽  
Tensor Square

We consider stationary stochastic processes $\{X_{n}:n\in \mathbb{Z}\}$ such that $X_{0}$ lies in the closed linear span of $\{X_{n}:n\neq 0\}$; following Ghosh and Peres, we call such processes linearly rigid. Using a criterion of Kolmogorov, we show that it suffices, for a stationary stochastic process to be linearly rigid, that the spectral density vanishes at zero and belongs to the Zygmund class $\unicode[STIX]{x1D6EC}_{\ast }(1)$. We next give a sufficient condition for stationary determinantal point processes on $\mathbb{Z}$ and on $\mathbb{R}$ to be linearly rigid. Finally, we show that the determinantal point process on $\mathbb{R}^{2}$ induced by a tensor square of Dyson sine kernels is not linearly rigid.

Discrete time point processes in urban traffic queue estimation

1978 ◽  
Author(s):  
J. Baras ◽  
W. Levine ◽  
T. Lin
Keyword(s):  
Discrete Time ◽  
Point Processes ◽  
Urban Traffic ◽  
Time Point

scholarly journals Extended and conditional versions of the PASTA property

1990 ◽  
Vol 22 (2) ◽  
pp. 510-512 ◽  
Author(s):  
Dieter König ◽  
Volker Schmidt
Keyword(s):  
Stochastic Processes ◽  
Point Processes ◽  
Long Run ◽  
Run Time

Two types of conditions are discussed ensuring the equality between long-run time fractions and long-run event fractions of stochastic processes with embedded point processes. Modifications of this equality statement are considered.

scholarly journals An online change detection test for parametric discrete-time stochastic processes

2018 ◽  
Vol 37 (2) ◽  
pp. 246-267
Author(s):  
Fanni K. Nedényi
Keyword(s):  
Change Detection ◽  
Stochastic Processes ◽  
Discrete Time ◽  
Online Change Detection

scholarly journals Learning Theory Estimates with Observations from General Stationary Stochastic Processes

2016 ◽  
Vol 28 (12) ◽  
pp. 2853-2889 ◽  
Author(s):  
Hanyuan Hang ◽  
Yunlong Feng ◽  
Ingo Steinwart ◽  
Johan A. K. Suykens
Keyword(s):  
Stochastic Processes ◽  
Type Inequality ◽  
Empirical Risk Minimization ◽  
Risk Minimization ◽  
Mixing Processes ◽  
Gaussian Kernels ◽  
Empirical Risk ◽  
Learning Rates ◽  
Stationary Stochastic Processes ◽  
Learning Schemes

This letter investigates the supervised learning problem with observations drawn from certain general stationary stochastic processes. Here by general, we mean that many stationary stochastic processes can be included. We show that when the stochastic processes satisfy a generalized Bernstein-type inequality, a unified treatment on analyzing the learning schemes with various mixing processes can be conducted and a sharp oracle inequality for generic regularized empirical risk minimization schemes can be established. The obtained oracle inequality is then applied to derive convergence rates for several learning schemes such as empirical risk minimization (ERM), least squares support vector machines (LS-SVMs) using given generic kernels, and SVMs using gaussian kernels for both least squares and quantile regression. It turns out that for independent and identically distributed (i.i.d.) processes, our learning rates for ERM recover the optimal rates. For non-i.i.d. processes, including geometrically [Formula: see text]-mixing Markov processes, geometrically [Formula: see text]-mixing processes with restricted decay, [Formula: see text]-mixing processes, and (time-reversed) geometrically [Formula: see text]-mixing processes, our learning rates for SVMs with gaussian kernels match, up to some arbitrarily small extra term in the exponent, the optimal rates. For the remaining cases, our rates are at least close to the optimal rates. As a by-product, the assumed generalized Bernstein-type inequality also provides an interpretation of the so-called effective number of observations for various mixing processes.

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