In this paper we establish the uniqueness of the Lamperti transformation leading from self-simila... more In this paper we establish the uniqueness of the Lamperti transformation leading from self-similar to stationary processes, and conversely. We discuss alpha-stable processes, which allow to understand better the difference between the Gaussian and non-Gaussian cases. As a by-product we get a natural construction of two distinct alpha-stable Ornstein–Uhlenbeck processes via the Lamperti transformation for 0 < alpha < 2. Also a new class of mixed linear fractional alpha-stable motions is introduced.
In the article we consider accumulated values of an- nuities-certain with yearly payments with in... more In the article we consider accumulated values of an- nuities-certain with yearly payments with independent random interest rates. We focus on general annuities with payments varying in arith- metic and geometric progression which are important varying annui- ties. We derive, via recursive relationships, mean and variance for- mulae of the final values of the annuities. Special cases of our results correct main outcome of Zaks (4).
In this paper we establish the uniqueness of the Lamperti transformation leading from self-simila... more In this paper we establish the uniqueness of the Lamperti transformation leading from self-similar to stationary processes, and conversely. We discuss alpha-stable processes, which allow to understand better the difference between the Gaussian and non-Gaussian cases. As a by-product we get a natural construction of two distinct alpha-stable Ornstein–Uhlenbeck processes via the Lamperti transformation for 0 < alpha < 2. Also a new class of mixed linear fractional alpha-stable motions is introduced.
In the article we consider accumulated values of an- nuities-certain with yearly payments with in... more In the article we consider accumulated values of an- nuities-certain with yearly payments with independent random interest rates. We focus on general annuities with payments varying in arith- metic and geometric progression which are important varying annui- ties. We derive, via recursive relationships, mean and variance for- mulae of the final values of the annuities. Special cases of our results correct main outcome of Zaks (4).
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Papers by A. Weron