Work

Approximation and estimation of scale functions for spectrally negative Levy processes

Year: 2024

Type: preprint

Abstract: The scale function holds significant importance within the fluctuation theory of Levy processes, particularly in addressing exit problems. However, its definition is established through the Laplace transform, thereby lacking explicit representations in general. This paper introduces a novel series representation for this scale function, employing Laguerre polynomials to construct a uniformly convergent approximate sequence. Additionally, we derive statistical inference based on specific discrete observations, presenting estimators of scale functions that are asymptotically normal.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2402.13599

Authors: Irie, Haruka, Shimizu, Yasutaka

Institution: Waseda University

Language: English

Topic: Probability and Risk Models

Subfield: Management Science and Operations Research

Field: Decision Sciences

Domain: Social Sciences

Open Access status: green

Funders: Japan Society for the Promotion of Science, Japan Science and Technology Agency, Core Research for Evolutional Science and Technology

Awards: G2521286739, G4397140745, 大規模時空間従属性データ科学へ向けた先端的確率統計学の新展開, An asymptotic distributional approach to the estimation error for expected functionals of generalized random elements, G6718509927, G7939374355

OpenAlex ID: W4392089901

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