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euler.py
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euler.py
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# Copyright 2020 Google LLC
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from .. import base_solver
from ...settings import SDE_TYPES, NOISE_TYPES, LEVY_AREA_APPROXIMATIONS
class Euler(base_solver.BaseSDESolver):
weak_order = 1.0
sde_type = SDE_TYPES.ito
noise_types = NOISE_TYPES.all()
levy_area_approximations = LEVY_AREA_APPROXIMATIONS.all()
def __init__(self, sde, **kwargs):
self.strong_order = 1.0 if sde.noise_type == NOISE_TYPES.additive else 0.5
super(Euler, self).__init__(sde=sde, **kwargs)
def step(self, t0, t1, y0, extra0):
del extra0
dt = t1 - t0
I_k = self.bm(t0, t1)
f, g_prod = self.sde.f_and_g_prod(t0, y0, I_k)
y1 = y0 + f * dt + g_prod
return y1, ()