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Mean exit time for stochastic dynamical systems driven by tempered stable Lévy fluctuations [article]

Yanjie Zhang, Xiao Wang, Jinqiao Duan
2019 arXiv   pre-print
We use the mean exit time to quantify macroscopic dynamical behaviors of stochastic dynamical systems driven by tempered L\'evy fluctuations, which are solutions of nonlocal elliptic equations.  ...  Firstly, we construct a new numerical scheme to compute and solve the mean exit time associated with the one dimensional stochastic system.  ...  one dimensional stochastic dynamical system with a scalar tempered Lévy fluctuation.  ... 
arXiv:1811.01634v2 fatcat:5ebpyeqjkjgzrcms2v5odixriy

Mean exit time and escape probability for the anomalous processes with the tempered power-law waiting times

Weihua Deng, Xiaochao Wu, Wanli Wang
2017 Europhysics letters  
from one region to another for a stochastic system driven by discontinuous (with jumps) Lévy motion.  ...  This paper discusses the two deterministic quantities, mean first exit time and escape probability, for the anomalous processes having the tempered Lévy stable waiting times with the tempering index λ>  ...  The mean first exit time is discussed for two models, namely, the coupled Langevin equation driven by Gaussian white noise and the one by non-Gaussian β-stable (0 < β < 2) Lévy noise.  ... 
doi:10.1209/0295-5075/117/10009 fatcat:hkqhhaqrxbcuvco4p46c7y6duu

Dynamics of Stochastic Reaction-Diffusion Equations [article]

Christian Kuehn, Alexandra Neamtu
2019 arXiv   pre-print
stochastic analysis, dynamics and applications.  ...  The main goal of this work is to provide a survey on different approaches to solution theory and dynamical properties for SPDEs, which is accessible for a wide community interested in modern methods in  ...  Hannelore Lisei for the kind invitation to contribute to the book Finite and Infinite Dimensional Stochastic Equations with Applications in Physics.  ... 
arXiv:1908.09177v1 fatcat:4ycp43flmbd2dd26c7tj57774q

Edge states in the climate system: exploring global instabilities and critical transitions

Valerio Lucarini, Tamás Bódai
2017 Nonlinearity  
Following an idea developed by Eckhardt and co. for the investigation of multistable turbulent flows, we study the global instability giving rise to the snowball/warm multistability in the climate system  ...  We also discover a new stable climatic state characterized by non-trivial symmetry properties.  ...  for providing insightful comments on the manuscript; and to L von Trier for directing and producing the movie Melancholia.  ... 
doi:10.1088/1361-6544/aa6b11 fatcat:sz4vpgblejhs5fh7ow6p546qc4

Seventeenth conference on stochastic processes and their applications

1990 Stochastic Processes and their Applications  
We survey several probabilistic models for images A new example of chaotic representation P.A. Meyer, Universite' L.  ...  .)), where v"( .) are the random broken lines constructed in the usual way by vh, k = 1,2,. , rl. Assume that the distribution of 1/, is absolutely continuous and has the finite variation.  ...  of the stochastic dynamical system 333-348.  ... 
doi:10.1016/0304-4149(90)90016-l fatcat:ikmobalwljelhhocel2r7b6rhi

A Pricing Measure to Explain the Risk Premium in Power Markets

Fred Espen Benth, Salvador Ortiz-Latorre
2014 SIAM Journal on Financial Mathematics  
Finally, our pricing measure allows us to have a stationary spot dynamics while still having randomly fluctuating forward prices for contracts far from maturity.  ...  The other factor is an OU process driven by a pure jump Lévy process and models the characteristic spikes observed in such markets.  ...  Obviously, we can choose β 2 = 1 and obtain similarly a nonstationary dynamics for the jump component as well; however, this will not be driven by a Lévy process under Qθ ,β .  ... 
doi:10.1137/13093604x fatcat:2vl57vrmmnedfawb7bk32ws4g4

On Fitting Finite Dirichlet Mixture Using ECM and MML [chapter]

Nizar Bouguila, Djemel Ziou
2005 Lecture Notes in Computer Science  
The system is analysed for different active periods corresponding to the service time of an M/G/1 queue and the busy period of an M/G/1 queue.  ...  During active periods, which are controlled by an exponential timer, there is a steady inflow into the fluid buffer at rate c0 and there is a steady outflow at rate c1 from the system when the buffer is  ...  These models are stochastic diffusion processes driven by α-stable (not necessarily symmetric) Lévy processes, with the drift given by a potential function.  ... 
doi:10.1007/11551188_19 fatcat:gtzi5u6emvfyxea3zbklobnvom

The large deviation approach to statistical mechanics

Hugo Touchette
2009 Physics reports  
The problems and results treated cover a wide range of physical systems, including equilibrium many-particle systems, noise-perturbed dynamics, nonequilibrium systems, as well as multifractals, disordered  ...  The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems.  ...  Kiessling for reading the manuscript. A special thank is also due to Ana Belinda Peñalver Peña for her more than needed support.  ... 
doi:10.1016/j.physrep.2009.05.002 fatcat:ao4p4q7qg5ffpkrmcguug5augi

The Physics of Climate Variability and Climate Change [article]

Michael Ghil, Valerio Lucarini
2020 arXiv   pre-print
Recent advances in the application of dynamical systems theory, on the one hand, and of nonequilibrium statistical physics, on the other, are brought together for the first time and shown to complement  ...  The system exhibits natural variability on many scales of motion, in time as well as space, and it is subject to various external forcings, natural as well as anthropogenic.  ...  For the time being, such a data-driven forecast appears to still be quite competitive with those made by high-end, detailed GCMs (Barnston et al., 2012) .  ... 
arXiv:1910.00583v2 fatcat:thxqlbypwnf33pjfnoev25jdbi

Random walk algorithm for the Dirichlet problem for parabolic integro-differential equation [article]

G. Deligiannidis, S. Maurer, M.V. Tretyakov
2020 arXiv   pre-print
We consider stochastic differential equations driven by a general L\'evy processes (SDEs) with infinite activity and the related, via the Feynman-Kac formula, Dirichlet problem for parabolic integro-differential  ...  The method is based on three ingredients: (i) we approximate small jumps by a diffusion; (ii) we use restricted jump-adaptive time-stepping; and (iii) between the jumps we exploit a weak Euler approximation  ...  Introduction Stochastic differential equations driven by Lévy processes (SDEs) have become a very important modelling tool in finance, physics, and biology (see e.g. [1, 4, 6, 23] ).  ... 
arXiv:2001.05531v1 fatcat:fejkmyghojahlnvvkgqd74ryni


2017 Annals of Actuarial Science  
Single copies of the papers listed here can be obtained, subject to copyright law, by contacting the libraries. There may be a charge for this service.  ...  Members of the Institute and Faculty of Actuaries can also access these journals directly by registering for the eLibrary. A password is available on request.  ...  This paper is devoted to asymptotic analysis for a multi-dimensional risk model with a general dependence structure and stochastic return driven by a geometric Lévy process.  ... 
doi:10.1017/s1748499517000033 fatcat:5kodefwt6nf2hlapj7z6mqtefa

Social physics [article]

Marko Jusup, Petter Holme, Kiyoshi Kanazawa, Misako Takayasu, Ivan Romic, Zhen Wang, Suncana Gecek, Tomislav Lipic, Boris Podobnik, Lin Wang, Wei Luo, Tin Klanjscek (+3 others)
2021 arXiv   pre-print
Such a rise is driven both by physicists venturing outside of their traditional domain of interest, but also by scientists from other domains who wish to mimic the enormous success of physics throughout  ...  We do so by comprehensively (but not exhaustively) reviewing the current state of the art.  ...  Future outlook So far, the physics of urban systems has not been driven by a paramount goal.  ... 
arXiv:2110.01866v1 fatcat:ccfxyezl6zgddd6uvrxubmaxua


2012 Annals of Actuarial Science  
Issues may be borrowed by members.  ...  The market model is complete, continuous, the uncertainty is driven by Brownian motion and the stock price has mean reverting drift.  ...  We investigate a Black-Scholes financial model with stochastic coefficients and a payment process with death, survival and annuity claims driven by a point process with a stochastic intensity.  ... 
doi:10.1017/s1748499512000309 fatcat:npuvnlcspjhlngqxuwmuejsegy

Extremes and Recurrence in Dynamical Systems [article]

Valerio Lucarini, Davide Faranda, Ana Cristina Moreira Freitas, Jorge Milhazes Freitas, Tobias Kuna, Mark Holland, Matthew Nicol, Mike Todd, Sandro Vaienti
2016 arXiv   pre-print
detail the relationship between the hitting and return time statistics of a dynamical system and the possibility of constructing extreme value laws for given observables.  ...  Explicit derivation of extreme value laws are then provided for selected dynamical systems.  ...  Specific acknowledgements are reported below separately for each of the authors.  ... 
arXiv:1605.07006v1 fatcat:vgnkbvyehzasfoyg4zfu66ekee

Behavioral Approach to Market and Default Risks Modeling

Chamberlain Sylvain Taguedong
2009 Social Science Research Network  
BLS) and Moody's Analytics for their feedbacks during the explorative phase of this project, they gave a twist to the scope of the project. Chapter 1.  ...  The initial project was a study of the most popular risk measures with assets' dynamics linked to main fundamental exogenous risks. Which turned out too complex after an explorative analysis.  ...  Acknowledgements I thank my brothers and sisters for their support; my Dear friend, the Chartered Accountant Elvira Siani;  ... 
doi:10.2139/ssrn.1528569 fatcat:r4slemkrf5eyzcg4dx7nnphdeu
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