Representations of continuous additive functionals of zero energy via convolution type transforms of brownian local times and the radon transform

1994 ◽  
Vol 48 (1-2) ◽  
pp. 1-15 ◽  
Author(s):  
Toshio Yamada
Keyword(s):  
Radon Transform ◽  
Convolution Type ◽  
Local Times ◽  
Zero Energy ◽  
Additive Functionals

scholarly journals Occupation time problem for multifractional Brownian motion

2019 ◽  
Vol 39 (1) ◽  
pp. 99-113
Author(s):  
Mohamed Ait Ouahra ◽  
Raby Guerbaz ◽  
Hanae Ouahhabi ◽  
Aissa Sghir
Keyword(s):  
Brownian Motion ◽  
Sample Path ◽  
Local Limit ◽  
Continuous Functions ◽  
Occupation Time ◽  
Local Times ◽  
Additive Functionals ◽  
Multifractional Brownian Motion ◽  
Sample Path Properties ◽  
Time Problem

In this paper, by using a Fourier analytic approach, we investigate sample path properties of the fractional derivatives of multifractional Brownian motion local times. We also show that those additive functionals satisfy a property of local asymptotic self-similarity. As a consequence, we derive some local limit theorems for the occupation time of multifractional Brownian motion in the space of continuous functions. 

scholarly journals Stochastic calculus over symmetric Markov processes with time reversal

2015 ◽  
Vol 220 ◽  
pp. 91-148
Author(s):  
K. Kuwae
Keyword(s):  
Markov Processes ◽  
Time Reversal ◽  
Harmonic Functions ◽  
Stochastic Calculus ◽  
Additive Functional ◽  
Zero Energy ◽  
Additive Functionals ◽  
Stochastic Characterization ◽  
Symmetric Markov Processes

AbstractWe develop stochastic calculus for symmetric Markov processes in terms of time reversal operators. For this, we introduce the notion of the progressively additive functional in the strong sense with time-reversible defining sets. Most additive functionals can be regarded as such functionals. We obtain a refined formula between stochastic integrals by martingale additive functionals and those by Nakao's divergence-like continuous additive functionals of zero energy. As an application, we give a stochastic characterization of harmonic functions on a domain with respect to the infinitesimal generator of semigroup on L2-space obtained by lower-order perturbations.

scholarly journals The gauge theorem for a class of additive functionals of zero energy

1993 ◽  
Vol 97 (1-2) ◽  
pp. 195-210
Author(s):  
Joseph Glover ◽  
Murali Rao ◽  
Renming Song
Keyword(s):  
Zero Energy ◽  
Additive Functionals

scholarly journals Approximation of fractional local times: Zero energy and derivatives

2021 ◽  
Vol 31 (5) ◽  
Author(s):  
Arturo Jaramillo ◽  
Ivan Nourdin ◽  
Giovanni Peccati
Keyword(s):  
Local Times ◽  
Zero Energy

scholarly journals The gauge theorem for a class of additive functionals of zero energy

1994 ◽  
Vol 98 (4) ◽  
pp. 567-567
Author(s):  
Joseph Glover ◽  
Murali Rao ◽  
Renming Song
Keyword(s):  
Zero Energy ◽  
Additive Functionals
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