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Subordinator
About: Subordinator is a research topic. Over the lifetime, 771 publications have been published within this topic receiving 15383 citations.
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TL;DR: A fractional Feynman-Kac formula is utilized to show that weak ergodicity breaking of the FGCP depends on the existence of the subordinator and/or the divergence of variance.
Abstract: This paper presents a fractional generalized Cauchy process (FGCP) with an additive and a multiplicative Gaussian white noise for describing subordinated anomalous fluctuations. The FGCP displays intermittent dynamics on random time durations, whose analytical representation is given by the Ito[over ] stochastic integral. The associated probability density function is given by a generalized Cauchy distribution at the stationary state. A fractional Feynman-Kac formula is utilized to show that weak ergodicity breaking of the FGCP depends on the existence of the subordinator and/or the divergence of variance.
1 citations
TL;DR: In this article, the authors developed an approach to the study of the Feynman-Kac transform for non-Markov anomalous processes using methods from stochastic analysis.
Abstract: We develop a new approach to the study of the Feynman--Kac transform for non-Markov anomalous process $Y_t=X_{E_t}$ using methods from stochastic analysis, where $X$ is a strong Markov process on a...
1 citations
TL;DR: In this article, the extinction time of logistic branching processes in an independent random environment driven by a Brownian motion was studied. And the Laplace transform of the absorption time was derived as a functional of the solution to a Ricatti differential equation.
Abstract: In this paper, we study the extinction time of logistic branching processes which are perturbed by an independent random environment driven by a Brownian motion. Our arguments use a Lamperti-type representation which is interesting on its own right and provides a one to one correspondence between the latter family of processes and the family of Feller diffusions which are perturbed by an independent spectrally positive Levy process. When the independent random perturbation (of the Feller diffusion) is driven by a subordinator then the logistic branching processes in a Brownian environment converges to a specified distribution; otherwise, it becomes extinct a.s. In the latter scenario, and following a similar approach to [Lambert, Ann. Appl. Probab, 2005], we provide the expectation and the Laplace transform of the absorption time, as a functional of the solution to a Ricatti differential equation. In particular, the latter characterises the law of the process coming down from infinity.
1 citations
TL;DR: In this paper , the authors studied the probability that a bivariate subordinator (Y,Z) issued from 0 creeps through a graph in terms of its renewal function and the drifts of the components $Y$ and $Z$.
Abstract: A L\'evy process is said to creep through a curve if, at its first passage time across this curve, the process reaches it with positive probability. We first study this property for bivariate subordinators. Given the graph $\{(t,f(t)):t\ge0\}$ of any continuous, non increasing function $f$ such that $f(0)>0$, we give an expression of the probability that a bivariate subordinator $(Y,Z)$ issued from 0 creeps through this graph in terms of its renewal function and the drifts of the components $Y$ and $Z$. We apply this result to the creeping probability of any real L\'evy process through the graph of any continuous, non increasing function at a time where the process also reaches its past supremum. This probability involves the density of the renewal function of the bivariate upward ladder process as well as its drift coefficients. We also investigate the case of L\'evy processes conditioned to stay positive creeping at their last passage time below the graph of a function. Then we provide some examples and we give an application to the probability of creeping through fixed levels by stable Ornstein-Uhlenbeck processes. We also raise a couple of open questions along the text.
1 citations
TL;DR: In this article , the authors studied complex spatial diffusion equations with time-fractional derivative and studied their stochastic solutions, in particular, the integral operator solution to the heat-type equation where the time derivative is replaced with the convolution-type generalization of the regularized Caputo derivative.
Abstract: Abstract We deal with complex spatial diffusion equations with time-fractional derivative and study their stochastic solutions. In particular, we complexify the integral operator solution to the heat-type equation where the time derivative is replaced with the convolution-type generalization of the regularized Caputo derivative. We prove that this operator is solution of a complex time-fractional heat equation with complex spatial variable. This approach leads to a wrapped Brownian motion on a circle time-changed by the inverse of the related subordinator. This time-changed Brownian motion is analyzed and, in particular, some results on its moments, as well as its construction as weak limit of continuous-time random walks, are obtained. The extension of our approach to the higher dimensional case is also provided.
1 citations