Zobrazeno 1 - 10
of 21
pro vyhledávání: '"Cázares, Jorge Ignacio González"'
This paper provides an exact simulation algorithm for the sampling from the joint law of the first-passage time, the undershoot and the overshoot of a subordinator crossing a non-increasing boundary. We prove that the running time of this algorithm h
Externí odkaz:
http://arxiv.org/abs/2306.06927
We construct a fast exact algorithm for the simulation of the first-passage time, jointly with the undershoot and overshoot, of a tempered stable subordinator over an arbitrary non-increasing absolutely continuous function. We prove that the running
Externí odkaz:
http://arxiv.org/abs/2303.11964
We characterise, in terms of their transition laws, the class of one-dimensional L\'evy processes whose graph has a continuously differentiable (planar) convex hull. We show that this phenomenon is exhibited by a broad class of infinite variation L\'
Externí odkaz:
http://arxiv.org/abs/2205.14416
Publikováno v:
Annales Henri Lebesgue, 5 (2022)
We establish distributional limit theorems for the shape statistics of a concave majorant (i.e. the fluctuations of its length, its supremum, the time it is attained and its value at $T$) of any L\'evy process on $[0,T]$ as $T\to\infty$. The scale of
Externí odkaz:
http://arxiv.org/abs/2106.09066
Publikováno v:
ALEA, Lat. Am. J. Probab. Math. Stat. 19 (2022) 983-999
We establish a novel characterisation of the law of the convex minorant of any L\'evy process. Our self-contained elementary proof is based on the analysis of piecewise linear convex functions and requires only very basic properties of L\'evy process
Externí odkaz:
http://arxiv.org/abs/2105.15060
Publikováno v:
Statistics & Probability Letters (2021)
Without higher moment assumptions, this note establishes the decay of the Kolmogorov distance in a central limit theorem for L\'evy processes. This theorem can be viewed as a continuous-time extension of the classical random walk result by Friedman,
Externí odkaz:
http://arxiv.org/abs/2104.13855
Publikováno v:
Advances in Applied Probability, p. 1-28 (2023)
We develop a novel Monte Carlo algorithm for the vector consisting of the supremum, the time at which the supremum is attained and the position at a given (constant) time of an exponentially tempered L\'evy process. The algorithm, based on the increm
Externí odkaz:
http://arxiv.org/abs/2103.15310
Publikováno v:
Electron. J. Probab. 25 (2020) 1-33
Using marked Dirichlet processes we characterise the law of the convex minorant of the meander for a certain class of L\'evy processes, which includes subordinated stable and symmetric L\'evy processes. We apply this characterisaiton to construct $\v
Externí odkaz:
http://arxiv.org/abs/1910.13273
Publikováno v:
Mathematics of Operations Research 47(2) (2022) 1141-1168
We develop a novel approximate simulation algorithm for the joint law of the position, the running supremum and the time of the supremum of a general L\'evy process at an arbitrary finite time. We identify the law of the error in simple terms. We pro
Externí odkaz:
http://arxiv.org/abs/1810.11039
Publikováno v:
Adv. in Appl. Probab. 51 (2019), no. 4, 967-993
We exhibit an exact simulation algorithm for the supremum of a stable process over a finite time interval using dominated coupling from the past (DCFTP). We establish a novel perpetuity equation for the supremum (via the representation of the concave
Externí odkaz:
http://arxiv.org/abs/1806.01870