Field theoretic approach to master equations and a variational method beyond Poisson ansatz
نویسنده
چکیده
We develop a variational scheme in a field theoretic approach to a stochastic process. While various stochastic processes can be expressed by master equations, in general it is difficult to solve the master equations exactly, and it is also hard to solve the master equations numerically because of the curse of dimensionality. The field theoretic approach has been used in order to study such complicated master equations, and the variational scheme achieves tremendous reduction in the dimensionality of master equations. For the variational method, only the Poisson ansatz has been used, in which one restricts the variational function to a Poisson distribution. Hence, one has dealt with only restricted fluctuation effects. We develop the variational method further, which enables us to treat an arbitrary variational function. It is shown that the developed variational scheme gives a quantitatively good approximation for master equations which describe a stochastic gene regulatory network. Field theoretic approach to master equations and a variational method beyond Poisson ansatz2
منابع مشابه
A field theoretic approach to master equations and a variational method beyond the Poisson ansatz
We develop a variational scheme in a field theoretic approach to a stochastic process. While various stochastic processes can be expressed using master equations, in general it is difficult to solve the master equations exactly, and it is also hard to solve the master equations numerically because of the curse of dimensionality. The field theoretic approach has been used in order to study such ...
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