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Davar Khoshnevisan is a mathematician whose work concerns probability theory, particularly random fields and stochastic partial differential equations. His institutional page lists research on long-time behavior and well-posedness of randomly forced equations, as well as geometric properties of their solutions.^[ref]

His Topics in Probability: Lévy Processes by Davar Khoshnevisan develops how processes with stationary independent increments are decomposed and described by their exponents. For instance, the notes distinguish increasing jump processes through the Laplace exponent of a subordinator of a subordinator, connecting an abstract stochastic process to an explicitly computable transform.^[ref]

For a finite-valued subordinator $T$ starting at zero, the Laplace exponent of a subordinator is the function $\Phi$ determined byIts Lévy–Khintchine formula takes the formwhere $d$ is the deterministic drift coefficient and $\nu$ is the Lévy measure. This representation separates steady motion of the clock from its positive jumps.^[ref]

For a deterministic clock $T_t=dt$, $\Phi (\lambda )=d\lambda$. For a Poisson process of rate $a$ with unit jumps, $\Phi (\lambda )=a(1-e^{-\lambda })$. For a sum of independent subordinators, the Laplace exponent of a subordinator is the sum of the individual functions, because the Laplace transforms multiply. The transform at $\lambda =0$ gives $\Phi (0)=0$.

A subordinator is a Lévy process with nondecreasing paths. Its nonnegative stationary increments have a Laplace transform of the formwhere $\Phi$ is called its Laplace exponent. Its standard path convention is càdlàg. Subordinators provide random clocks for subordination of a Lévy process.