Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  develop a novel framework for formulating a class of stochastic reachability problems with state constraints as a stochastic optimal control problem. Previous approaches to solving these problems are either confined to the deterministic setting or address almost-sure stochastic notions. In contrast,  propose a new methodology to tackle probabilistic specifications that are less specific than almost sure requirements. To this end,  first establish a connection beten two stochastic reach-avoid problems and a class of stochastic optimal control problems for diffusions with discontinuous payoff functions.  then derive a ak version of dynamic programming principle (DPP) for the value function. Moreover, based on our DPP,  give an alternate characterization of the value function as the solution to a partial differential equation in the sense of discontinuous viscosity solutions. Finally  validate the performance of the proposed framework on the stochastic Zermelo navigation problem.
['Peyman Mohajerin Esfahani', 'Debasish Chatterjee', 'John Lygeros']
I am writing a research paper on a idea On a problem of stochastic reach-avoid set characterization
[{"from": "human", "value": "I am writing a research paper on a idea On a problem of stochastic reach-avoid set characterization"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  develop a novel framework for formulating a class of stochastic reachability problems with state constraints as a stochastic optimal control problem. Previous approaches to solving these problems are either confined to the deterministic setting or address almost-sure stochastic notions. In contrast,  propose a new methodology to tackle probabilistic specifications that are less specific than almost sure requirements. To this end,  first establish a connection beten two stochastic reach-avoid problems and a class of stochastic optimal control problems for diffusions with discontinuous payoff functions.  then derive a ak version of dynamic programming principle (DPP) for the value function. Moreover, based on our DPP,  give an alternate characterization of the value function as the solution to a partial differential equation in the sense of discontinuous viscosity solutions. Finally  validate the performance of the proposed framework on the stochastic Zermelo navigation problem."}]