113 research outputs found
Jump-type Hunt processes generated by lower bounded semi-Dirichlet forms
Let be a locally compact separable metric space and be a positive
Radon measure on it. Given a nonnegative function defined on
off the diagonal whose anti-symmetric part is assumed to be less singular than
the symmetric part, we construct an associated regular lower bounded
semi-Dirichlet form on producing a Hunt process on
whose jump behaviours are governed by . For an arbitrary open subset
, we also construct a Hunt process on in an analogous
manner. When is relatively compact, we show that is censored in
the sense that it admits no killing inside and killed only when the path
approaches to the boundary. When is a -dimensional Euclidean space and
is the Lebesgue measure, a typical example of is the stable-like
process that will be also identified with the solution of a martingale problem
up to an -polar set of starting points. Approachability to the boundary
in finite time of its censored process on a bounded open
subset will be examined in terms of the polarity of for the
symmetric stable processes with indices that bound the variable exponent
.Comment: Published in at http://dx.doi.org/10.1214/10-AOP633 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
On the conservativeness and the recurrence of symmetric jump-diffusions
Sufficient conditions for a symmetric jump-diffusion process to be
conservative and recurrent are given in terms of the volume of the state space
and the jump kernel of the process. A number of examples are presented to
illustrate the optimality of these conditions; in particular, the situation is
allowed to be that the state space is topologically disconnected but the
particles can jump from a connected component to the other components.Comment: 22 page
Perturbation approach to the Feller property for non-local operators (Stochastic Analysis of Jump Processes and Related Topics)
SIGLEAvailable from British Library Document Supply Centre- DSC:DXN054819 / BLDSC - British Library Document Supply CentreGBUnited Kingdo
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