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We consider a continuous time version of Cramers theorem with nonnegative summands $ S_t=frac{1}{t}sum_{i:tau_ile t}xi_i, t toinfty, $ where $(tau_i,xi_i)_{ige 1}$ is a sequence of random variables such that $tS_t$ is a random process with independent increments.
In this paper, we consider the product space for two processes with independent increments under nonlinear expectations. By introducing a discretization method, we construct a nonlinear expectation under which the given two processes can be seen as a new process with independent increments.
In this paper, we study unitary Gaussian processes with independent increments with which the unitary equivalence to a Hudson-Parthasarathy evolution systems is proved. This gives a generalization of results in [16] and [17] in the absence of the stationarity condition.
This is a continuation of the earlier work cite{SSS} to characterize stationary unitary increment Gaussian processes. The earlier assumption of uniform continuity is replaced by weak continuity and with a technical assumption on the domain of the gen
The aim of this article is to characterize unitary increment process by a quantum stochastic integral representation on symmetric Fock space. Under certain assumptions we have proved its unitary equivalence to a Hudson-Parthasarathy flow.
We prove that a positive self-similar Markov process $(X,mathbb{P})$ that hits 0 in a finite time admits a self-similar recurrent extension that leaves 0 continuously if and only if the underlying L{e}vy process satisfies Cram{e}rs condition.