Topic
Subordinator
About: Subordinator is a research topic. Over the lifetime, 771 publications have been published within this topic receiving 15383 citations.
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01 Jan 2008
TL;DR: In this article, the authors apply a dierential calculus for linear operators, together with moduli of smoothness techniques, in order to obtain Edgeworth expansions for E`(Z(t)) i E´(Z), where Z is a standard normal variable.
Abstract: We apply a dierential calculus for linear operators, together with moduli of smooth- ness techniques, in order to obtain Edgeworth expansions for E`(Z(t)) i E`(Z), where (Z(t); t ‚ 1) is a standardized subordinator, Z is a standard normal ran- dom variable and the degree of smoothness ofgoes from infinite dierentiability to bounded variation. The main achievement of the method is to provide explicit upper bounds for the remainders, thus getting rid o the 'big or little o' terms. Other features are the relative simplicity of the proofs, the property of monotonic convergence for E`(Z(t)) under simple sucient conditions on ` and, in the lattice case, the obtention of explicit lower and upper Berry-Esseen bounds of the same order of magnitude which are asymptotically sharp.
2 citations
TL;DR: For increasing sequences tk, this paper gave normalizing constants tk such that tk→∞ t−1X(tk) is a.s constant, and also derived upper bounds.
Abstract: Let {X(t): 0≤t<∞) be a stable subordinator with α∈(0,1). For increasing sequences tk we give normalizing constants ak such thatliminfk→∞ ak−1X(tk) is a.s constant. We also derive a.s. upper bounds.
2 citations
25 May 2006
TL;DR: In this paper, a simpler and shorter proof of Kesten's result for the probabilities with which a subordinator hits points is given, where the probability of hitting a point is proportional to the probability that the subordinator is hit.
Abstract: We give a simpler and shorter proof of Kesten's result for the probabilities with which a subordinator hits points.
2 citations
TL;DR: The rates of strong convergence for various approximation schemes are investigated for a class of stochastic differential equations (SDEs) which involve a random time change given by an inverse subordinator.
Abstract: The rates of strong convergence for various approximation schemes are investigated for a class of stochastic differential equations (SDEs) which involve a random time change given by an inverse subordinator. SDEs to be considered are unique in two different aspects: (i) they contain two drift terms, one driven by the random time change and the other driven by a regular, non-random time variable; (ii) the standard Lipschitz assumption is replaced by that with a time-varying Lipschitz bound. The difficulty imposed by the first aspect is overcome via an approach that is significantly different from a well-known method based on the so-called duality principle. On the other hand, the second aspect requires the establishment of a criterion for the existence of exponential moments of functions of the random time change.
2 citations
TL;DR: A new model which is time driven model for option pricing is proposed, in this model, the price of underlying asset is driven by different random driving source in different time interval.
Abstract: A new model which we called time driven model for option pricing is proposed. In this model, the price of underlying asset is driven by different random driving source in different time interval. E...
2 citations