Numerical Modelling of Random Processes and Fields: Algorithms and Applications - V. A. Ogorodnikov; S. M. Prigarin.
Stability Problems for Stochastic Models - V.V. Kalashnikov; V. M. Zolotarev .
On characterizations of interpolable and minimal stationary processes
On a topological characterization of simple closed curve on the plane
The article contains no abstract
q-variate minimal stationary processes
Aronszajn-Kolmogorov type theorems for positive definite kernels in locally convex spaces
On measure-preserving transformations and doubly stationary symmetric stable processes
In a 1987 paper, Cambanis, Hardin and Weron defined doubly stationary stable processes as those stable processes which have a spectral representation which is itself stationary, and they gave an example of a stationary symmetric stable process which they claimed was not doubly stationary. Here we show that their process actually had a moving average representation, and hence was doubly stationary. We also characterize doubly stationary processes in terms of measure-preserving regular set isomorphisms...
Dilations of Banach space operator valued functions
Pricing forward-start options in the HJM framework; evidence from the Polish market
We show how to use the Gaussian HJM model to price modified forward-start options. Using data from the Polish market we calibrate the model and price this exotic option on the term structure. The specific problems of Central Eastern European emerging markets do not permit the use of the popular lognormal models of forward LIBOR or swap rates. We show how to overcome this difficulty.
Fractional Langevin equation with α-stable noise. A link to fractional ARIMA time series
We introduce a fractional Langevin equation with α-stable noise and show that its solution is the stationary α-stable Ornstein-Uhlenbeck-type process recently studied by Taqqu and Wolpert. We examine the asymptotic dependence structure of via the measure of its codependence r(θ₁,θ₂,t). We prove that is not a long-memory process in the sense of r(θ₁,θ₂,t). However, we find two natural continuous-time analogues of fractional ARIMA time series with long memory in the framework of the Langevin...
Integrals related to stationary processes and cylindrical martingales
Banach-space-valued stationary processes and their linear prediction
Contents0. Introduction............................................................................................................................................. 51. Linear operators generated by random elements.......................................................................... 62. Covariance operator of generalized random elements................................................................. 93. The space of generalized random elements of the second-order as an LVH-space.................
Chaotic behavior of infinitely divisible processes
The hierarchy of chaotic properties of symmetric infinitely divisible stationary processes is studied in the language of their stochastic representation. The structure of the Musielak-Orlicz space in this representation is exploited here.
Bounded solutions for ARMA model with varying coefficients
The paper deals with ARMA systems of equations with varying coefficients. A complete description of bounded solutions to ARMA(1,q) systems is obtained and their uniqueness is studied. Some special cases are discussed, including the case of significant interest of systems with periodic coefficients. The paper generalizes results of [9] and opens a new direction of study.
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