Time Changes of Symmetric Markov Processes

2011 ◽  
Author(s):  
Zhen-Qing Chen ◽  
Masatoshi Fukushima
Keyword(s):  
Markov Processes ◽  
Dirichlet Form ◽  
Dirichlet Space ◽  
Energy Functional ◽  
Brownian Motions ◽  
Joint Distributions ◽  
Open Set ◽  
Symmetric Markov Processes ◽  
Time Changes

This chapter discusses the time change. It first relates the perturbation of the Dirichlet form to a Feynman-Kac transform of X and deals with characterization of the Dirichlet form (Ĕ,̆‎F) of a time-changed process. The chapter next introduces the concept of the energy functional of a general symmetric transient right process, as well Feller measures on F relative to the part process X⁰ of X on the quasi open set E₀ = E∖F. It derives the Beurling-Deny decomposition of the extended Dirichlet space (̆Fₑ,Ĕ) living on F in terms of the due restriction of E to F with additional contributions by Feller measures. Finally, Feller measures are described probabilistically as the joint distributions of starting and end points of the excursions of the process X away from the set F using an associated exit system. Examples related to Brownian motions and reflecting Brownian motions are also provided.

Basic Properties and Examples of Dirichlet Forms

2011 ◽  
Author(s):  
Zhen-Qing Chen ◽  
Masatoshi Fukushima
Keyword(s):  
Markov Process ◽  
Potential Theory ◽  
Dirichlet Form ◽  
Dirichlet Space ◽  
Dirichlet Forms ◽  
Dirichlet Spaces ◽  
Basic Properties ◽  
Time Changes ◽  
Symmetric Operators ◽  
Analytic Potential

This chapter introduces the concepts of the transience, recurrence, and irreducibility of the semigroup for general Markovian symmetric operators and presents their characterizations by means of the associated Dirichlet form as well as the associated extended Dirichlet space. These notions are invariant under the time changes of the associated Markov process. The chapter then presents some basic examples of Dirichlet forms, with special attention paid to their basic properties as well as explicit expressions of the corresponding extended Dirichlet spaces. Hereafter the chapter discusses the analytic potential theory for regular Dirichlet forms, and presents some conditions for the demonstrated Dirichlet form (E,F) to be local.

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 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.

Cumulative constrained sojourn times in semi-Markov processes with an application to pensionable service

1978 ◽  
Vol 15 (3) ◽  
pp. 531-542 ◽  
Author(s):  
Izzet Sahin
Keyword(s):  
Markov Processes ◽  
Sojourn Time ◽  
Working Life ◽  
Partial Coverage ◽  
Sojourn Times ◽  
Semi Markov Processes

This paper is concerned with the characterization of the cumulative pensionable service over an individual's working life that is made up of random lengths of service in different employments in a given industry, under partial coverage, transferability, and a uniform vesting rule. This characterization uses some results that are developed in the paper involving a functional and cumulative constrained sojourn times (constrained in the sense that if a sojourn time is less than a given constant it is not counted) in semi-Markov processes.

scholarly journals Synthesis and Optical Characterization of Carbon Dot from Peels of Dragon Fruit and Pear

2018 ◽  
Vol 4 (1) ◽  
pp. 19 ◽  
Author(s):  
Selvy Uftovia Hepriyadi ◽  
. Isnaeni
Keyword(s):  
Carbon Dots ◽  
Optical Characterization ◽  
Heating Time ◽  
Emission Wavelength ◽  
Time Resolved ◽  
Carbon Dot ◽  
Infrared Wavelength ◽  
Dragon Fruit ◽  
Time Changes

Fluorescence materials such as carbon dots are unique and non-toxic materials that can be produced using many methods. In this research, synthesis and optical characterization of carbon dots from the peels of dragon fruit and pear have been done. The synthesis uses bottom-up method using microwave with 20 minutes, 40 minutes, and 80 minutes of heating time. The result of optical characterizations showed that the samples that have been heat treated are carbon dots based of the absorbance in the range of 280-350 nm, and the intensity are decreased in the range of visible and infrared wavelength. There are emission and intensity changes by different heat treatments. From the samples of dragon fruit's peels, the emission wavelength tended to shift toward visible light at the wavelength of 551.51 nm, 507.98 nm and 487.28 nm with the excitation at the wavelength of 420 nm from pulsed pico-laser. While, the emission wavelength from the samples of pears peels were fluctuate in wavelength of 529.09 nm, 507.52 nm and 519.46 nm. Similarly, the time-resolved photoluminescence characterization test showed that there were time changes in each sample of carbon dot. The decay lifetime of carbon dots was fluctuated between 4.5 ns - 5.4 ns for dragon fruit’s peels and about 1.9 ns - 2.4 ns for pear's peels.

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