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Theory and applications of Lévy processes (stochastic processes with stationary and independent increments): e.g. path properties, stochastic differential equations driven by jump-type processes, fluctuation theory of Lévy processes, queuing theory.
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Injectivity of a convolution operator
Let $V(\mu)=\sqrt{\mu} L_2\subset L_1$ (with Lebesgue measure) and $V'(\mu)$ be a dual of $V'(\mu)$ with respect to pairing $(f,v) = \int f v dx$. The set $V'(\mu)$ can be thought of as $\frac{\chi_{\ …