131 research outputs found
Bismut Formulae and Applications for Functional SPDEs
By using Malliavin calculus, explicit derivative formulae are established for
a class of semi-linear functional stochastic partial differential equations
with additive or multiplicative noise. As applications, gradient estimates and
Harnack inequalities are derived for the semigroup of the associated segment
process. Keywords: Bismut formula, Malliavin calculus, gradient estimate,
Harnack inequality, functional SPDEComment: 14 page
Derivative Formula and Harnack Inequality for Degenerate Functional SDEs
By constructing successful couplings, the derivative formula, gradient
estimates and Harnack inequalities are established for the semigroup associated
with a class of degenerate functional stochastic differential equations.Comment: 20 page
Exponential Mixing for Retarded Stochastic Differential Equations
In this paper, we discuss exponential mixing property for Markovian
semigroups generated by segment processes associated with several class of
retarded Stochastic Differential Equations (SDEs) which cover SDEs with
constant/variable/distributed time-lags. In particular, we investigate the
exponential mixing property for (a) non-autonomous retarded SDEs by the
Arzel\`{a}--Ascoli tightness characterization of the space \C equipped with
the uniform topology (b) neutral SDEs with continuous sample paths by a
generalized Razumikhin-type argument and a stability-in-distribution approach
and (c) jump-diffusion retarded SDEs by the Kurtz criterion of tightness for
the space \D endowed with the Skorohod topology.Comment: 20 page
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