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We investigate a theoretical framework to solve partial differential equations by using stochastic processes, e.g., chemical reaction systems. The framework is based on ‘duality’ concept in stochastic processes, which has been widely studied and used in mathematics and physics. Using the duality concept, a partial differential equation is connected to a stochastic process via a duality function. Without...
In the context of Markov processes, we show a new scheme to derive dual processes and a duality function based on a boson representation. This scheme is applicable to a case in which a generator is expressed by boson creation and annihilation operators. For some stochastic processes, duality relations have been known, which connect continuous time Markov processes with discrete state space and those...
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