Self-Similar Processes with Stationary Increments
(1/α)-Self similar α-stable processes with stationary increments
... The class of a-stable H-self-similar processes with stationary increments ( H-sssi processes) has been extensively studied in recent years.. to show that two such s[r] ...
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Non-stationary self-similar Gaussian processes as scaling limits of power law shot noise processes and generalizations of fractional Brownian motion
... noise processes introduces new classes of self-similar Gaussian processes that have non-stationary ...new self-similar processes in Section ...these ...
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Discrete approximation of a stable self-similar stationary increments process
... stable self-similar stationary increments ...such processes were intensively investigated, but lit- tle is known on the context in which such processes can ...
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Distribution processes with stationary fractional increments
... distribution processes we began to study in 2] and 1]. These processes form a sub-family of the Gelfand-Vilenkin's family (5]) because the underlying continuity holds with relation to a stronger ...
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Power variation for Gaussian processes with stationary increments
... the processes X = φ • G, where G is a Gaussian process with stationary ...the increments of G and certain regularity conditions on the path of the process φ we prove the convergence in probability ...
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Path Behavior of Processes with Stationary Independent Increments
... By Corollary 4.1, stationarity and strong Markov, it follows that zk(o3 ) will exceed 1 for sufficiently large k. This completes the proof.. Path Behavior of Processes with Sta[r] ...
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Robust Extrapolation Problem for Stochastic Processes with Stationary Increments
... stochastic processes is an important part of the theory of stochastic pro- ...stochastic processes were developed by Kolmogorov [1], Wiener[2], Yaglom [3, ...non-stationary processes whose in- ...
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The Lamperti transformation for self-similar processes
... from self-similar to stationary processes, and ...α-stable processes, which allow to understand better the difference between the Gaussian and non- Gaussian ...Ornstein–Uhlenbeck ...
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Methods for analysis of functionals on Gaussian self similar processes
... 1.1 Standard and Anomalous diffusion processes The concept of diffusion is widely used in physical sciences, economics and finance. However, in each case, the object (e.g., atom, price, etc.) that is undergoing ...
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Parisian ruin of self-similar Gaussian risk processes
... the self-similar Gaussian risk process R u is defined as τ u ∗ = inf { t ≥ T u : t − κ t,u ≥ T u } , with κ t,u = sup { s ∈ [0, t] : R u (s) ≥ 0 } ...
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Self similar Markov processes and the time inversion property
... stochastic processes, we are often looking for some property seen empirically in experiment that can be used to provide tractability in our ...these increments often appear independent of each ...evy ...
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Have the log population processes stationary and independent increments? Empirical evidence for Italy, Spain and the USA along more than a century
... of processes embrace as particular cases the geometric Brownian motion (with a Yule process, possibly) or geometric Brownian process with drift and/or Pois- son ...of increments of the ...
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From infinite urn schemes to self-similar stable processes
... new processes in this family are still being discovered ...stable processes is via the flow representation, introduced by Rosi´ nski [20] and developed by Samorodnitsky [21], of the corresponding increment ...
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STOCHASTIC MODEL ON FINDING STATIONARY INCREMENTS OF WATER LEVEL IN METTUR DAM DURING JUNE 2005-MAY 2006 USING GAUSSIAN PROCESSES
... In India water resources are increasingly becoming scarce. Since rainfall occurs only for three months in a few spells, storage by dams is imperative to utilize waters defined in [1]. The Mettur dam is one of the ...
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Some Convergence Results On Stable Infinite Moving Average Processes And Stable Self-Similar Processes
... a stationary time series have infinite vari- ance, as is the case with linear processes with SαS noise, the notions of auto- covariance, autocorrelation and spectral distribution are not applicable ...
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Clustering piecewise stationary processes
... Index Terms—stationary ergodic processes, unsupervised learning, clustering, consistency I. I NTRODUCTION Clustering involves breaking a dataset into disjoint subsets called clusters where the elements ...
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Inversion, duality and Doob h transforms for self similar Markov processes
... the self-similarity property is essential in these path ...of self-similar Markov ...any self-similar Markov process absorbed at 0 can be represented as a time changed Markov additive ...
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From infinite urn schemes to decompositions of self-similar Gaussian processes
... the similar flavor of the Hammond–Sheffield model that scales to a fractional Brownian motion with Hurst index H ∈ (0, 1/2) , the alternative assigning rule is crucial, while the underlying random graph with long ...
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Minimum distance estimation of stationary and non-stationary ARFIMA processes
... the parameters. With the exception of Japan, it seems to be the case that Canada and Germany are clear cases where the GDP per capita series are fractionally integrated, with a value of d around 0.5 for the former and in ...
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Nonstationary increments, scaling distributions, and variable diffusion processes in financial markets
... Arguably the most important problem in quantitative finance is to under- stand the nature of stochastic processes that underlie market dynamics. One aspect of the solution to this problem involves determining ...
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