Last Updated：2022/12/23
Sentence
We
also
build
a
partial
link
between
energy
solutions
as
introduced
by
Goncalves
and
Jara
and
paracontrolled
solutions.
Interpreting
the
KPZ
equation
as
the
value
function
of
an
optimal
control
problem,
we
give
a
pathwise
proof
for
the
global
existence
of
solutions
and
thus
for
the
strict
positivity
of
solutions
to
the
stochastic
heat
equation.
Moreover,
we
study
Sasamoto-Spohn
type
discretizations
of
the
stochastic
Burgers
equation
and
show
that
their
limit
solves
the
continuous
Burgers
equation
possibly
with
an
additional
linear
transport
term.
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We also build a partial link between energy solutions as introduced by Goncalves and Jara and paracontrolled solutions. Interpreting the KPZ equation as the value function of an optimal control problem, we give a pathwise proof for the global existence of solutions and thus for the strict positivity of solutions to the stochastic heat equation. Moreover, we study Sasamoto-Spohn type discretizations of the stochastic Burgers equation and show that their limit solves the continuous Burgers equation possibly with an additional linear transport term.
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