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Article overview
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Redundant basis interpretation of Doi-Peliti method and an application | | Shunta Takahashi
; Jun Ohkubo
; | | Date: |
1 Sep 2023 | | Abstract: | The Doi-Peliti method is effective for investigating classical stochastic
processes, and it has wide applications, including field theoretic approaches.
Furthermore, it is applicable not only to master equations but also to
stochastic differential equations; one can derive a kind of discrete process
from stochastic differential equations. A remarkable fact is that the
Doi-Peliti method is related to a different analytical approach, i.e.,
generating function. The connection with the generating function approach helps
to understand the derivation of discrete processes from stochastic differential
equations. Here, a redundant basis interpretation for the Doi-Peliti method is
proposed, which enables us to derive different types of discrete processes. The
conventional correspondence with the generating function approach is also
extended. The proposed extensions give us a new tool to study stochastic
differential equations. As an application of the proposed interpretation, we
perform numerical experiments for a finite-state approximation of the derived
discrete process from the noisy van der Pol system; the redundant basis yields
reasonable results compared with the conventional discrete process with the
same number of states. | | Source: | arXiv, 2309.00253 | | Services: | Forum | Review | PDF | Favorites | |
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