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I am wondering whether anyone knows if the square of Dirac Delta function is defined somewhere. In the beginning, this question might look strange. But by restricting the space of the test functions, ...

Consider the following one dimensional Young differential equation: \begin{align*} &Y_t=\int_0^t Y_s dX_s,\quad t\in[0,1];\\ &Y_0=0. \end{align*} Here the driving process $X$ is a bounded ...

I am trying to understand the mathod of characteristics for solving partial differential equations. However, all the examples I found over the internet are for first order PDEs or for second order ...