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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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TL;DR: For a class of Laplace exponents, the authors derived explicit approximate expressions for these objects in the form of asymptotic expansions via the saddle point method for the subordinator's transition density and via the Mellin transform for the subordinate heat kernel.
Abstract: For a class of Laplace exponents, we consider the transition density of the subordinator and the heat kernel of the corresponding subordinate Brownian motion. We derive explicit approximate expressions for these objects in the form of asymptotic expansions: via the saddle point method for the subordinator’s transition density and via the Mellin transform for the subordinate heat kernel. The latter builds on ideas from index theory using zeta functions. In either case, we highlight the role played by the analyticity of the Laplace exponent for the qualitative properties of the asymptotics.
5 citations
TL;DR: In this paper, the authors considered the stochastic Lotka-Volterra model with additive jump noises and derived the likelihood function and explicit estimator by using semimartingale theory.
Abstract: In this paper, we consider the stochastic Lotka–Volterra model with additive jump noises. We show some desired properties of the solution such as existence and uniqueness of positive strong solution, unique stationary distribution, and exponential ergodicity. After that, we investigate the maximum likelihood estimation for the drift coefficients based on continuous time observations. The likelihood function and explicit estimator are derived by using semimartingale theory. In addition, consistency and asymptotic normality of the estimator are proved. Finally, computer simulations are presented to illustrate our results.
5 citations
TL;DR: In this paper, the authors develop an equilibrium endowment economy with Epstein-Zin recursive utility and a Levy time-change subordinator, which represents a clock that connects business and calendar time.
5 citations
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TL;DR: In this paper, the Riesz-Feller derivative was used to obtain the transition semigroup of a stable process subordinated by an independent gamma subordinator with drift, which is represented by the so-called Poisson process with drift.
Abstract: We deal with some extensions of the space-fractional diffusion equation, which is satisfied by the density of a stable process (see Mainardi, Luchko, Pagnini (2001)): the first equation considered here is obtained by adding an exponential differential operator expressed in terms of the Riesz-Feller derivative. We prove that this produces a random additional term in the time-argument of the corresponding stable process, which is represented by the so-called Poisson process with drift. Analogously, if we add, to the space-fractional diffusion equation, a logarithmic differential operator involving the Riesz-derivative, we obtain, as a solution, the transition semigroup of a stable process subordinated by an independent gamma subordinator with drift. Finally, we show that a non-linear extension of the space-fractional diffusion equation is satisfied by the transition density of the process obtained by time-changing the stable process with an independent linear birth process with drift.
5 citations
TL;DR: In this paper, the authors derived the heat trace asymptotics of the generator of subordinate Brownian motion on Euclidean space for a class of Laplace exponents.
Abstract: We derive the heat trace asymptotics of the generator of subordinate Brownian motion on Euclidean space for a class of Laplace exponents. The terms in the asymptotic expansion can be computed to arbitrary order and depend both on the geometry of Euclidean space and the short-time behaviour of the process. If the Blumenthal-Getoor index of the process is rational, then the asymptotics may contain logarithmic terms. The key assumption is the existence of a suitable density for the Levy measure of the subordinator. The analysis is highly explicit.
4 citations