Exponential asymptotics for intersection local times of stable processes and random walks
Exponential ergodicity of semilinear equations driven by Lévy processes in Hilbert spaces
We study convergence to the invariant measure for a class of semilinear stochastic evolution equations driven by Lévy noise, including the case of cylindrical noise. For a certain class of equations we prove the exponential rate of convergence in the norm of total variation. Our general result is applied to a number of specific equations driven by cylindrical symmetric α-stable noise and/or cylindrical Wiener noise. We also consider the case of a "singular" Wiener process with unbounded covariance...
Exponential functionals of Lev́y processes.
Exponential inequalities and functional central limit theorems for random fields
We establish new exponential inequalities for partial sums of random fields. Next, using classical chaining arguments, we give sufficient conditions for partial sum processes indexed by large classes of sets to converge to a set-indexed brownian motion. For stationary fields of bounded random variables, the condition is expressed in terms of a series of conditional expectations. For non-uniform -mixing random fields, we require both finite fourth moments and an algebraic decay of the mixing coefficients....
Exponential inequalities and functional central limit theorems for random fields
We establish new exponential inequalities for partial sums of random fields. Next, using classical chaining arguments, we give sufficient conditions for partial sum processes indexed by large classes of sets to converge to a set-indexed Brownian motion. For stationary fields of bounded random variables, the condition is expressed in terms of a series of conditional expectations. For non-uniform ϕ-mixing random fields, we require both finite fourth moments and an algebraic decay of the mixing coefficients. ...
Exponential inequalities for self-normalized processes with applications.
Exponential inequalities for sums of weakly dependent variables.
Exponential inequalities for VLMC empirical trees
A seminal paper by Rissanen, published in 1983, introduced the class of Variable Length Markov Chains and the algorithm Context which estimates the probabilistic tree generating the chain. Even if the subject was recently considered in several papers, the central question of the rate of convergence of the algorithm remained open. This is the question we address here. We provide an exponential upper bound for the probability of incorrect estimation of the probabilistic tree, as a function...
Exponential martingales and CIR model
With the use of exponential martingales and the Girsanov theorem we show how to calculate bond prices in a large variety of square root processes. We clarify and correct several errors that abound in financial literature concerning these processes. The most important topics are linear risk premia, the Longstaff double square model, and calculations concerning correlated CIR processes.
Exponential smoothing for irregular data
Various types of exponential smoothing for data observed at irregular time intervals are surveyed. Double exponential smoothing and some modifications of Holt’s method for this type of data are suggested. A real data example compares double exponential smoothing and Wright’s modification of Holt’s method for data observed at irregular time intervals.
Exponential smoothing for irregular time series
The paper deals with extensions of exponential smoothing type methods for univariate time series with irregular observations. An alternative method to Wright’s modification of simple exponential smoothing based on the corresponding ARIMA process is suggested. Exponential smoothing of order m for irregular data is derived. A similar method using a DLS **discounted least squares** estimation of polynomial trend of order m is derived as well. Maximum likelihood parameters estimation for forecasting...
Exponential smoothing for time series with outliers
Recursive time series methods are very popular due to their numerical simplicity. Their theoretical background is usually based on Kalman filtering in state space models (mostly in dynamic linear systems). However, in time series practice one must face frequently to outlying values (outliers), which require applying special methods of robust statistics. In the paper a simple robustification of Kalman filter is suggested using a simple truncation of the recursive residuals. Then this concept is applied...
Exponentielle stochastique et intégrale multiplicative discontinues
Exponentielles et fonctionnelles de Schwinger en analyse gaussienne non commutative
Exposants critiques pour le mouvement brownien et les marches aléatoires
Extending Lévy's characterisation of brownian motion
Extending probability spaces and adapted distribution
Extensions of measures and abstract stochastic processes
Extrapolation in fractional autoregressive models
The naïve and the least-squares extrapolation are investigated in the fractional autoregressive models of the first order. Some explicit formulas are derived for the one and two steps ahead extrapolation.
Extrapolation of moving average and autoregressive processes when the entire past of the processes is known.