<i>Harmonic Analysis and the Theory of Probability</i>

Bochner, S.; Teichmann, T.

doi:10.1063/1.3059907

Cited by 265 publications

(191 citation statements)

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“…The present paper can be regarded as a complement the latter investigations as we consider certain jump processes on closed manifolds. Subordination in the sense of Bochner [7] allows to construct new stochastic processes from a given process using a random time change. On the level of generators of the corresponding semigroups, this translates to a functional calculus, cf.…”

Section: Introductionmentioning

confidence: 99%

Off-Diagonal Heat Kernel Asymptotics of Pseudodifferential Operators on Closed Manifolds and Subordinate Brownian Motion

Fahrenwaldt

2017

Integr. Equ. Oper. Theory

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Abstract.We derive the off-diagonal short-time asymptotics of the heat kernels of functions of generalised Laplacians on a closed manifold. As an intermediate step we give an explicit asymptotic series for the kernels of the complex powers of generalised Laplacians. Each asymptotic series is formulated in terms of the geodesic distance. The key application concerns upper bounds for the transition density of subordinate Brownian motion. The approach is highly explicit and tractable.Mathematics Subject Classification. Primary 35K08; Secondary 58J65, 35S05.

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Section: Introductionmentioning

confidence: 99%

Off-Diagonal Heat Kernel Asymptotics of Pseudodifferential Operators on Closed Manifolds and Subordinate Brownian Motion

Fahrenwaldt

2017

Integr. Equ. Oper. Theory

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“…The new process is called subordinate. The idea of subordination was introduced in 1949 by Bochner [12] and expounded in his book in [13]. The theory of subordinated processes is also explored in details in [14].…”

Section: Introductionmentioning

confidence: 99%

Arithmetic Brownian motion subordinated by tempered stable and inverse tempered stable processes

Wyłomańska

2012

Physica A: Statistical Mechanics and its Applications

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In the last decade the subordinated processes have become popular and found many practical applications. Therefore in this paper we examine two processes related to time-changed (subordinated) classical Brownian motion with drift (called arithmetic Brownian motion). The first one, so called normal tempered stable, is related to the tempered stable subordinator, while the second one -to the inverse tempered stable process. We compare the main properties (such as probability density functions, Laplace transforms, ensemble averaged mean squared displacements) of such two subordinated processes and propose the parameters' estimation procedures. Moreover we calibrate the analyzed systems to real data related to indoor air quality.

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“…Subordination, i.e. where the chronometer is a Lévy process independent of the base process and the base process is a Lévy process or, more generally, a time-homogeneous Markov process, is a classical area, initiated by Bochner (1949Bochner ( ,1955; some recent references are Bertoin (1996Bertoin ( ,1997, Sato (1999), and Barndorff-Nielsen, Pedersen and Sato (2001). There is a wide range of Lévy processes, obtained by subordination of Brownian motion, which are of interest as models in mathematical finance.…”

Section: Introductionmentioning

confidence: 99%

Infinite Divisibility for Stochastic Processes and Time Change

Barndorff–Nielsen

Maejima

Sato³

2006

J Theor Probab

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General results concerning infinite divisibility, selfdecomposability, and the class L m property as properties of stochastic processes are presented. A new concept called temporal selfdecomposability of stochastic processes is introduced. Lévy processes, additive processes, selfsimilar processes, and stationary processes of Ornstein-Uhlenbeck type are studied in relation to these concepts. In the latter half of the paper time change of stochastic processes is studied, where chronometers (stochastic processes that serve to change time) and base processes (processes to be time-changed) are independent but do not, in general, have independent increments. Conditions for inheritance of infinite divisibility and selfdecomposability under time change are given.

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Harmonic Analysis and the Theory of Probability

Cited by 265 publications

References 0 publications

Off-Diagonal Heat Kernel Asymptotics of Pseudodifferential Operators on Closed Manifolds and Subordinate Brownian Motion

Off-Diagonal Heat Kernel Asymptotics of Pseudodifferential Operators on Closed Manifolds and Subordinate Brownian Motion

Arithmetic Brownian motion subordinated by tempered stable and inverse tempered stable processes

Infinite Divisibility for Stochastic Processes and Time Change

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