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Stochastic process

About: Stochastic process is a research topic. Over the lifetime, 31227 publications have been published within this topic receiving 898736 citations. The topic is also known as: random process & stochastic processes.


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Journal ArticleDOI
TL;DR: In this paper, the Markov point processes introduced by Ripley & Kelly are generalised by replacing fixed-range spatial interactions by interactions between neighbouring particles, where the neighbourhood relation may depend on the point configuration.
Abstract: Summary The Markov point processes introduced by Ripley & Kelly are generalised by replacing fixed-range spatial interactions by interactions between neighbouring particles, where the neighbourhood relation may depend on the point configuration. The corresponding HammersleyClifford characterisation theorem is proved. The results are used to construct new models for point processes, multitype point processes and random processes of geometrical objects. Monte Carlo simulations of these models can be generated by running spatial birth-and-death processes.

198 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that the Navier-Stokes equations possess an exponentially attracting invariant measure, which is in fact the consequence of a more general ''Harris-like'' ergodic theorem applicable to many dissipative stochastic PDEs and processes with memory.
Abstract: We prove that the two dimensional Navier-Stokes equations possess an exponentially attracting invariant measure. This result is in fact the consequence of a more general ``Harris-like'' ergodic theorem applicable to many dissipative stochastic PDEs and stochastic processes with memory. A simple iterated map example is also presented to help build intuition and showcase the central ideas in a less encumbered setting. To analyze the iterated map, a general ``Doeblin-like'' theorem is proven. One of the main features of this paper is the novel coupling construction used to examine the ergodic theory of the non-Markovian processes.

197 citations

Journal ArticleDOI
TL;DR: In this article, a functional central limit theorem was proved for multivariate Hawkes processes observed over a time interval [ 0, T ] when T?? is a discrete scheme with mesh? over [ 0, T ] up to some further time shift.

197 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that high-order cumulants in the complex plane constitute a universal phenomenon, appearing as functions of almost any parameter, including time in the transient regime.
Abstract: Noise is a result of stochastic processes that originate from quantum or classical sources. Higher-order cumulants of the probability distribution underlying the stochastic events are believed to contain details that characterize the correlations within a given noise source and its interaction with the environment, but they are often difficult to measure. Here we report measurements of the transient cumulants n(m) of the number n of passed charges to very high orders (up to m = 15) for electron transport through a quantum dot. For large m, the cumulants display striking oscillations as functions of measurement time with magnitudes that grow factorially with m. Using mathematical properties of high-order derivatives in the complex plane we show that the oscillations of the cumulants in fact constitute a universal phenomenon, appearing as functions of almost any parameter, including time in the transient regime. These ubiquitous oscillations and the factorial growth are system-independent and our theory provides a unified interpretation of previous theoretical studies of high-order cumulants as well as our new experimental data.

197 citations

Journal ArticleDOI
TL;DR: This work solves completely the starting and stopping problem when the dynamics of the system are a general adapted stochastic process and uses backward stoChastic differential equations and Snell envelopes.
Abstract: In this work, we solve completely the starting and stopping problem when the dynamics of the system are a general adapted stochastic process. We use backward stochastic differential equations (BSDEs) and Snell envelopes. Finally, we give some numerical results.

197 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023159
2022355
2021985
20201,151
20191,119
20181,115