Stochastic processes and boundary value problems

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, some <a href="/facts/Boundary_value_problem/QEfmUqmP">boundary value problems</a> can be solved using the methods of <a href="/facts/Stochastic_processes/Ng1n1dnB">stochastic analysis</a>. Perhaps the most celebrated example is <a href="/facts/Shizuo_Kakutani/WGLekK88">Shizuo Kakutani</a>'s 1944 solution of the <a href="/facts/Dirichlet_problem/uHErgNCb">Dirichlet problem</a> for the <a href="/facts/Laplace_operator/kov9u3PT">Laplace operator</a> using <a href="/facts/Brownian_motion/Th0g0wkr">Brownian motion</a>. However, it turns out that for a large class of <a href="/facts/Semi-elliptic_operator/w8IkFPhn">semi-elliptic</a> second-order <a href="/facts/Partial_differential_equations/DyPsBlv7">partial differential equations</a> the associated Dirichlet boundary value problem can be solved using an <a href="/facts/It%C5%8D_process/2uSR02fY">Itō process</a> that solves an associated <a href="/facts/Stochastic_differential_equation/ol9a9WNq">stochastic differential equation</a>.
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Stochastic processes and boundary value problems open-in-new

Stochastic processes and boundary value problems