scholarly journals On the Laws of Total Local Times for -Paths and Bridges of Symmetric Lévy Processes

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Masafumi Hayashi ◽  
Kouji Yano
Keyword(s):  
Local Time ◽  
Lévy Processes ◽  
Levy Processes ◽  
Explicit Representation ◽  
Local Times ◽  
Bessel Processes ◽  
Single Level ◽  
The Law

The joint law of the total local times at two levels for -paths of symmetric Lévy processes is shown to admit an explicit representation in terms of the laws of the squared Bessel processes of dimensions two and zero. The law of the total local time at a single level for bridges is also discussed.

scholarly journals Regularity of Local Times Associated with Volterra–Lévy Processes and Path-Wise Regularization of Stochastic Differential Equations

2021 ◽  
Author(s):  
Fabian A. Harang ◽  
Chengcheng Ling
Keyword(s):  
Differential Equations ◽  
Local Time ◽  
Lévy Process ◽  
Lévy Processes ◽  
Levy Processes ◽  
Levy Process ◽  
Local Times ◽  
Volterra Kernel ◽  
Spatial Regularity ◽  
Regularizing Effects

AbstractWe investigate the space-time regularity of the local time associated with Volterra–Lévy processes, including Volterra processes driven by $$\alpha $$ α -stable processes for $$\alpha \in (0,2]$$ α ∈ ( 0 , 2 ] . We show that the spatial regularity of the local time for Volterra–Lévy process is $${\mathbb {P}}$$ P -a.s. inverse proportional to the singularity of the associated Volterra kernel. We apply our results to the investigation of path-wise regularizing effects obtained by perturbation of ordinary differential equations by a Volterra–Lévy process which has sufficiently regular local time. Following along the lines of Harang and Perkowski (2020), we show existence, uniqueness and differentiability of the flow associated with such equations.

scholarly journals Explicit Representation of the Minimal Variance Portfolio in Markets Driven by Levy Processes

2003 ◽  
Vol 13 (1) ◽  
pp. 55-72 ◽  
Author(s):  
Fred Espen Benth ◽  
Giulia Di Nunno ◽  
Arne Lokka ◽  
Bernt Oksendal ◽  
Frank Proske
Keyword(s):  
Lévy Processes ◽  
Levy Processes ◽  
Explicit Representation ◽  
Minimal Variance

scholarly journals Particle picture representation of the non-symmetric Rosenblatt process and Hermite processes of any order

2019 ◽  
Vol 19 (01) ◽  
pp. 1950001
Author(s):  
Łukasz Treszczotko
Keyword(s):  
Local Time ◽  
Lévy Processes ◽  
Levy Processes ◽  
Intersection Local Time ◽  
Rosenblatt Process ◽  
System Of Particles

We provide a particle picture representation for the non-symmetric Rosenblatt process and for Hermite processes of any order, extending the result of Bojdecki, Gorostiza and Talarczyk in [4]. We show that these processes can be obtained as limits of certain functionals of a system of particles evolving according to symmetric stable Lévy motions. In the case of [Formula: see text]-Hermite processes the corresponding functional involves [Formula: see text]-intersection local time of symmetric stable Lévy processes.

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