A further generalization of random self-decomposability
The notion of random self-decomposability is generalized further. The notion is then extended to non-negative integer-valued distributions.
math.PR↗
arXiv subjects
S Satheesh
Publications and source records attributed to S Satheesh.
A generalization of random self-decomposability
The notion of random self-decomposability is generalized here. Its relation to self-decomposability, Harris infinite divisibility and its connection with a stationary first order generalized autoregressive model are presented. The notion is then extended to $\mathbf{Z_+}$-valued distributions.
math.PR↗
Non-Negative Integer-Valued Semi-Selfsimilar Processes
Non-negative integer-valued semi-selfsimilar processes are introduced. Levy processes in this class are characterized. Its relation to an AR(1) scheme is derived.
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A Max-AR(1) Model with Max-Semistable Marginals
The structure of stationary first order max-autoregressive schemes with max-semi-stable marginals is studied. A connection between semi-selfsimilar extremal processes and this max-autoregressive scheme is discussed resulting in their characterizations. Corresponding cases of max-stable and selfsimilar extremal processes are also discussed.
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A Generalization of Stationary AR(1) Schemes
Here we develop a first order autoregressive model {Xn} that is marginally stationary where Xn is the sum/ extreme of k i.i.d observations. We prove that stationary solutions to these models are either semi-selfdecomposable/ extreme-semi-selfdecomposable or, sum/ extreme stable with respect to Harris distribution.
math.PR↗
On the Marginal Distributions of Stationary AR(1) Sequences
In this note we correct an omission in our paper (Satheesh and Sandhya, 2005) in defining semi-selfdecomposable laws and also show with examples that the marginal distributions of a stationary AR(1) process need not even be infinitely divisible.
math.PR↗
An Autoregressive Model with Semi-stable Marginals
The family of semi-stable laws is shown to be semi-selfdecomposable. Thus they qualify to model stationary first order autoregressive schemes. A connection between these autoregressive schemes with semi-stable marginals and semi-selfsimilar processes is given.
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A Generalization and Extension of an Autoregressive Model
Generalizations and extensions of a first order autoregressive model of Lawrance and Lewis (1981) are considered and characterized here.
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Semi-Selfdecomposable Laws and Related Processes
In this note we identify the class of distributions for {Xn} that can generate a linear, additive, first order auto-regressive scheme that is marginally stationary as semi-selfdecomposable laws. We give a method to construct these distributions. Its implications in subordination and selfdecomposability of Levy processes are given. The discrete analogues of these processes are also discussed.
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Max-Semi-Selfdecomposable Laws and Related Processes
Methods of construction of Max-semi-selfdecompsable laws are given. Implications of this method in random time changed extremal processes are discussed. Max-autoregressive model is introduced and characterized using the max-semi-selfdecompsable laws and exponential max-semi-stable laws. Max-semi-selfddecomposability of max-semi-stable laws are proved.
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Semi-Selfdecomposable Laws in the Minimum Scheme
We discuss semi-selfdecomposable laws in the minimum scheme and characterize them using an autoregressive model. Semi-Pareto and semi-Weibull laws of Pillai (1991) are shown to be semi-selfdecomposable in this scheme. Methods for deriving this class of laws are then attempted from the angle of randomization. Finally, discrete analogues of these results are also considered.
math.PR↗