  | 
	
	
	 | 
	 | 
	
		 |  |  |  |  | 	 | 
	 | 
	 | 
	
		
	 | 
	 | 
	 | 
	 
	
 
 
	
	    
Two-sided Estimates on the Density of the Feynman-Kac Semigroups of Stable-like Processes	   
  
	 | 
  
 
	  
		 
			
			   
Renming  Song, University of Illinois 			 | 
		  
	   
		
  
		
			 
				
					   
					   Abstract 
	In this paper we establish two-sided estimates for the density of
the Feynman-Kac semigroups of stable-like processes with potentials
given by signed measures belonging to the Kato class. We also provide
similar estimates for the densities of two other kinds of 
Feynman-Kac semigroups of stable-like processes.
				   
 
  
				 | 
			  
		   
   
Full text: PDF
  Pages: 146--161
  Published on: February 25, 2006
 
  
	 | 
 
 
                
                         
                                
                                          
                                           Bibliography 
        
- 
S. Albeverio and Z. M. Ma.
Perturbation of Dirichlet forms--lower semiboundedness,
closability and form cores.
J. Funct. Anal. 99 (1991), 332--356.
Math. Review 92i:47039
 - 
Ph. Blanchard and Z. M. Ma.
Semigroup of Schr"odinger operators with potentials given
by Radon measures. 
In  Stochastic processes, physics 
and geometry.  160--194,  World Sci. Publishing, Teaneck, NJ, 1990.
Math. Review 93a:35034
 - 
R. M. Blumenthal and R. K. Getoor.
Some theorems on stable processes.
Trans. Amer. Math. Soc. 95 (1960), 263--273.
Math. Review 0119247
 -  Z.-Q. Chen and T. Kumagai.
Heat kernel estimates for stable-like processes on $d$-sets.
 Stochastic Process. Appl. 108 (2003), 27--62.
Math. Review 2005d:60135
 -  Z.-Q. Chen and R. Song.
Intrinsic ultracontractivity and conditional gauge for symmetric 
stable processes.
 J. Funct. Anal. 150 (1997), 204--239.
Math. Review 98j:60103
 - 
 Z.-Q. Chen and R. Song.
Conditional gauge theorem for non-local Feynman-Kac
transforms.
 Probab. Th. rel. Fields 125 (2003), 45--72.
Math. Review 2003m:60213
 -  Z.-Q. Chen and T. Zhang.
Girsanov and Feynman-Kac type transformations for symmetric 
Markov processes.
 Ann. Inst. H. Poincar'e Probab. Statist.
38 (2002), 475--505.
Math. Review 2004e:60128
 - 
M. Fukushima.
On a decomposition of additive functionals in the strict sense
for a symmetric Markov process. 
In  Dirichlet forms and stochastic processes, 
155--169, de Gruyter, Berlin, 1995. 
Math. Review 97k:60210
 - 
M. Fukushima, Y. Oshima and M. Takeda.
 Dirichlet forms and symmetric Markov processes,
Walter De Gruyter, Berlin, 1994.
Math. Review 96f:60126
 - 
M. Sharpe.
 General Theory of Markov Processes,
Academic Press, Boston, 1988.
Math. Review 89m:60169
 -  B. Simon.
Schr"odinger semigroups.  
 Bull. Amer. Math. Soc. (N.S.) ,  
7 (1982), 447--526.
Math. Review 86b:81001a
 -  R. Song.
Feynman-Kac semigroup with discontinuous additive functionals.
 J. Theoret. Probab. 8 (1995), 727--762.
Math. Review 97a:60106
 - Qi S. Zhang. 
A Harnack inequality for the equation 
$nabla(anabla u)+bnabla u=0$, when $vert bvert in Ksb {n+1}$.
 Manuscripta Math.  89 (1996), 61--77.
Math. Review 97a:35045
 -  Qi S. Zhang. 
Gaussian bounds for the fundamental 
solutions of $nabla (Anabla u)+Bnabla u-usb t=0$. 
 Manuscripta Math.  93 (1997), 381--390. 
Math. Review 98c:35067
  
                                   
 
  
                                 | 
                          
                   
	  
 
 
 
 | 
		
			
 
 
 
 
 
 
 
 
  
			
			
			
			 
		 | 
		
	| 
	 | 
	
    	 
    	
  
     | 
     | 
 
	 | 
	
		 |  |  |  |  | 
 
 Electronic Journal of Probability.   ISSN: 1083-6489 	 | 
	 |