The first exit time of a biharmonic pseudo process and its application to the boundary value problems

半直线弯曲梁由结构端固定，其方程为四阶偏微分方程θ_tu（t，x）=-θ^4_xu（t，x）t>0，x>0θ^j_xu（t，0）=0 θ^k_xu（t，0）t>=0 t>0，其中（j，k）取自结构端在x=0处的组合：（j，k）=（0，1）;固定端（j，k）=（0，2）;对于每个（j，k），我们构造了满足随机边界条件的双调和伪过程{X^<（jk）>（t）}，它对应于上述方程.然后，我们研究了弯曲梁的精确运动，在分析了相应的{X^<（jk）>（t）}在边界处的行为之后。

A half line bending beam is fixed by a structural end, what is represented by the 4-th order partial differential equationθ_tu(t,x)=-θ^4_xu(t,x) t>0,x>0θ^j_xu(t,0)=0 θ^k_xu(t,0) t>=0 t>0,where (j,k) is taken from one of such combinations derived from structural ends at x=0 :(j,k)=(0,1) ; The fixed end, (j,k)=(0,2) ; The pinned end,(j,k)=(1,3) ; The side end, (j,k)=(2,3) ; The free endFor each (j,k), we constructed the diharmonic pseudo processes {X^<(jk)>(t)} which satisfies a stochastic boundary condition and corresponds to the above equation. Then, we investigated a precise motion of the bending beam, after analyzing behaviors of the corresponding {X^<(jk)>(t)} at the boundary.