Results 1  10
of
15
Conditional gauge theorem for nonlocal FeynmanKac transforms
 PROBAB. THEORY RELAT. FIELDS
, 2003
"... ..."
Girsanov And FeynmanKac Type Transformations For Symmetric Markov Processes
 Ann. Inst. H. Poincaré Probab. Statist
, 2002
"... Studied in this paper is the transformation of an arbitrary symmetric Markov process X by multiplicative functionals which are the exponential of continuous additive functionals of X having zero quadratic variations. We characterize the transformed semigroups by their associated quadratic forms. Thi ..."
Abstract

Cited by 15 (6 self)
 Add to MetaCart
(Show Context)
Studied in this paper is the transformation of an arbitrary symmetric Markov process X by multiplicative functionals which are the exponential of continuous additive functionals of X having zero quadratic variations. We characterize the transformed semigroups by their associated quadratic forms. This is done by rst identifying the symmetric Markov process under Girsanov transform, which may be of independent interest, and then applying FeynmanKac transform to the Girsanov transformed process. Stochastic analysis for discontinuous martingales is used in our approach.
A convergence theorem for Dirichlet forms with applications to boundary value problems with varying domains
 Math. Z
, 1995
"... ..."
The AllegrettoPiepenbrink Theorem for Strongly Local Dirichlet Forms
 DOCUMENTA MATH.
, 2009
"... The existence of positive weak solutions is related to spectral information on the corresponding partial differential operator. ..."
Abstract

Cited by 8 (6 self)
 Add to MetaCart
(Show Context)
The existence of positive weak solutions is related to spectral information on the corresponding partial differential operator.
Generalized eigenfunctions and spectral theory for strongly local Dirichlet forms
, 2009
"... We present an introduction to the framework of strongly local Dirichlet forms and discuss connections between the existence of certain generalized eigenfunctions and spectral properties within this framework. The range of applications is illustrated by a list of examples. ..."
Abstract

Cited by 8 (5 self)
 Add to MetaCart
(Show Context)
We present an introduction to the framework of strongly local Dirichlet forms and discuss connections between the existence of certain generalized eigenfunctions and spectral properties within this framework. The range of applications is illustrated by a list of examples.
ON THE RECONSTRUCTION OF THE DRIFT OF A DIFFUSION FROM TRANSITION PROBABILITIES WHICH ARE PARTIALLY OBSERVED IN SPACE
, 2004
"... Abstract. The problem of reconstructing the drift of a diffusion in R d, d≥2, from the transition probability density observed outside a domain is considered. The solution of this problem also solves a new inverse problem for a class of parabolic partial differential equations. This work considerabl ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
(Show Context)
Abstract. The problem of reconstructing the drift of a diffusion in R d, d≥2, from the transition probability density observed outside a domain is considered. The solution of this problem also solves a new inverse problem for a class of parabolic partial differential equations. This work considerably extends [2] in terms of generality, both concerning assumptions on the drift coefficient, and allowing for nonconstant diffusion coefficient. Sufficient conditions for solvability of this type of inverse problem for d = 1 are also given. 1.
LittlewoodPaley Inequality For A Diffusion Satisfying The Logarithmic Sobolev Inequality And For The Brownian Motion On A Riemannian Manifold With Boundary
, 2000
"... . We discuss the LittlewoodPaley inequality for a di usion process associated with a Dirichlet form of gradient type. We assume that the logarithmic Sobolev inequality holds and the negative part of # 2 is exponentially integrable. Under these and some additional conditions, we showed that ##u# p ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
(Show Context)
. We discuss the LittlewoodPaley inequality for a di usion process associated with a Dirichlet form of gradient type. We assume that the logarithmic Sobolev inequality holds and the negative part of # 2 is exponentially integrable. Under these and some additional conditions, we showed that ##u# p # C# # 1  Lu# q for 1 <p<q. We also discuss the Brownian motion on a Riemannian manifold with boundary. 1. Introduction In this paper, we discuss the LittlewoodPaley inequality.T ypical e ample is the Brownian motion on the Euclidean space and it leads to the following inequality: for any p>1 there exist a positive constant C such that C 1 ##u# p ## # #u# p # C##u# p . (1.1) # #, the square root of the minus Laplacian, is called the Cauchy operator. (1.1) is equivalent to the L p boundedness of the Riesz transformation. T#tr kind of inequality also holds for the OrnsteinUhlenbeck process on an abstract Wiener space, which was proved by P. A. Meyer [11] in a probabili...
On FeynmanKac perturbation of symmetric Markov processes
 Proceedings of Functional Analysis IX
, 2005
"... Let X be an msymmetric right process on Luzin space E and (E, F) be its associated quasiregular Dirichlet form. Let µ be a signed smooth measure of X and A µ be the continuous additive functional (CAF in abbreviation) of X with signed Revuz measure µ. It defines a symmetric FeynmanKac semigroup Tt ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
(Show Context)
Let X be an msymmetric right process on Luzin space E and (E, F) be its associated quasiregular Dirichlet form. Let µ be a signed smooth measure of X and A µ be the continuous additive functional (CAF in abbreviation) of X with signed Revuz measure µ. It defines a symmetric FeynmanKac semigroup Ttf(x): = Ex [exp(A µ t)f(Xt)] for t> 0 and f ≥ 0. (1) Define a symmetric quadratic form (E µ, D(E µ)) by D(E µ): = � u ∈ F: u ∈ L 2 (E, µ) �, E µ � (u, v) = E(u, v) − u(x)v(x)µ(dx) for u, v ∈ D(C). E We say that the form (E µ, D(E µ)) is bounded from below if there is some α0 ≥ 0 such that E µ α0 (u, u): = Eµ (u, u) + α0(u, u) ≥ 0 for every u ∈ D(E µ). For a nonnegative smooth measure ν, we say it is in the Kato class of X if lim t→0 sup [A x∈E ν t] = 0. It is known (see, e.g., [1, Proposition 2.1(i)] and [6, Theorem 3.1]) that if ν is in the Kato class of X, then for every ε> 0, there is some constant Aε> 0 such that u(x) 2 � ν(dx) ≤ ε E(u, u) + Aε u(x) 2 m(dx) for every u ∈ F.
Trace ideal properties of perturbed Dirichlet semigroups
 In Mathematical results in quantum mechanics (Proc. Blossin
, 1993
"... ..."
(Show Context)