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I saw this paper: https://arxiv.org/abs/1306.2382

Chatterjee gives a representation of many solutions of the wave equation in terms of Brownian motion. I haven't seen much other than this. Is there any recent developments?

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  • $\begingroup$ I am not sure about the state of the art, but there is a nice paper of Pal-Shkolnikov which shows hows hyperbolic PDE arise from intertwining relations between diffusion processes: arxiv.org/abs/1306.0857 $\endgroup$
    – Dan
    Commented Feb 10, 2020 at 15:39
  • $\begingroup$ Is Navier-Stokes considered Hyperbolic ? If yes, then see this:Constantin, Peter, and Gautam Iyer. "A stochastic Lagrangian representation of the three‐dimensional incompressible Navier‐Stokes equations." CPAM (2008) $\endgroup$
    – Piyush Grover
    Commented Feb 10, 2020 at 21:11

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