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Generalized Feynman-Kac Transformation and Fukashima's Decomposition for Nearly Symmetric Markov Processes

Title:

Generalized Feynman-Kac Transformation and Fukashima's Decomposition for Nearly Symmetric Markov Processes

Ma, Li (2011) Generalized Feynman-Kac Transformation and Fukashima's Decomposition for Nearly Symmetric Markov Processes. PhD thesis, Concordia University.

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Abstract

In this thesis, we study some problems about nearly symmetric Markov processes,which are associated with non-symmetric Dirichlet forms or semi-Dirichlet forms. For a Markov process (Xt, Px) associated with a non-symmetric Dirichlet form (E,D(E)) on L2(E;m), we study the strong continuity of the generalized Feynman- Kac semigroup (Pu
t )t≥0, which is defined by Pu t f(x) := Ex[eNu t f(Xt)], f ≥ 0 and t ≥ 0.Here u ∈ D(E), Nu t is the continuous additive functional of zero energy in the Fukushima’s decomposition. We give two sufficient conditions for (Pu
t )t≥0 to be strongly continuous.The first sufficient condition is that there exists a constant α0 ≥ 0 such that for any f ∈ D(E)b, Qu(f, f) ≥ −α0(f, f)m, where (Qu,D(E)b) is defined by Qu(f, g) := E(f, g) + E(u, fg), f,g∈ D(E)b := D(E) ∩ L∞(E;m). The second sufficient condition is that there exists a constant α0 ≥ 0 such that �Pu
t �2 ≤ eα0t, ∀t > 0. For a Markov process associated with a semi-Dirichlet form, we establish Fukushima’s
decomposition and give a transformation formula for local martingale additive functionals.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (PhD)
Authors:Ma, Li
Institution:Concordia University
Degree Name:Ph. D.
Program:Mathematics
Date:29 June 2011
Thesis Supervisor(s):Sun, Wei
Keywords:Dirichlet forms, strong continuous, generalized Feynman-Kac semigroup, semi-Dirichlet forms, Fukushima's decomposition, local martingale additive functionals, zero energy, transformation formula.
ID Code:7696
Deposited By:LI MA
Deposited On:22 Nov 2011 08:44
Last Modified:04 Jan 2012 15:06
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