We pose the problem of approximating optimally a given nonnegative signal with scalar autoconvolution signal. The I-divergence is chosen as optimality criterion being well suited to incorporate nonnegativity constraints. After proving existence an optimal approximation, we derive iterative descent algorithm alternating minimization type find minimizer. based on lifting technique developed by Cs...

In transactions associated with future-oriented financial instruments, such as options, a huge amount of data is available buried inside which the market's best guess to what future holds. We consider here possibility extracting foreign exchange volatility information from option aid new computational inverse algorithm using minimization convex functional.
 See also https://ejde.math.txsta...

The problem of minimizing or maximizing the time spent by a controlled diffusion process in given interval is known as LQG homing. optimal control, when it possible to obtain an explicit solution such problem, often expressed special functions. Here, inverse considered: we determine, under certain assumptions, processes for which control simple power function. Moreover, extended case jump-diffu...