207 research outputs found
Representation of functionals of Ito processes and their first exit times
The representation theorem is obtained for functionals of non-Markov
processes and their first exit times from bounded domains. These functionals
are represented via solutions of backward parabolic Ito equations. As an
example of applications, analogs of forward Kolmogorov equations are derived
for conditional probability density functions of Ito processes being killed on
the boundary. In addition, a maximum principle and a contraction property are
established for SPDEs in bounded domains.Comment: 25 page
On causal extrapolation of sequences with applications to forecasting
The paper suggests a method of extrapolation of notion of one-sided
semi-infinite sequences representing traces of two-sided band-limited
sequences; this features ensure uniqueness of this extrapolation and
possibility to use this for forecasting. This lead to a forecasting method for
more general sequences without this feature based on minimization of the mean
square error between the observed path and a predicable sequence. These
procedure involves calculation of this predictable path; the procedure can be
interpreted as causal smoothing. The corresponding smoothed sequences allow
unique extrapolations to future times that can be interpreted as optimal
forecasts.Comment: arXiv admin note: substantial text overlap with arXiv:1111.670
Duality and semi-group property for backward parabolic Ito equations
We study existence, uniqueness, semi-group property, and a priori estimates
for solutions for backward parabolic Ito equations in domains with boundary. We
study also duality between forward and backward equations. The semi-group for
backward equations is established in the form of some anti-causality. The
novelty is that the semi-group property involves the diffusion term that is a
part of the solution
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