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math.PR2026
On the First Hitting Time Problems for Diffusion Processes: Local Time-Space Approach
Jerome Detemple, Yerkin Kitapbayev, Danila Shabalin
Using the local time-space calculus of Peskir (2005) and the method developed in Mijatovic (2010), we derive a new integral representation for the backward probability associated w…
math.PR2026
Volterra Integral Reduction for Boundary Diffusion Problems
Danila Shabalin
This paper addresses a class of integral representations of the form \begin{equation} f(t,x)=g(t,x)+\int_0^t k(t,s)\, p(t-s,x,y)\, \partial_x f(s,y^+)\,ds, \qquad 0 \le t \le T, \e…