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Stochastic processes have wide relevance in mathematics both for theoretical aspects and for their numerous realworld applications in various domains. They represent a very active research field which is attracting the growing interest of scientists from a range of disciplines.This Special Issue aims to present a collection of current contributions concerning various topics related to stochastic processes and their applications. In particular, the focus here is on applications of stochastic processes as models of dynamic phenomena in research areas certain to be of interest, such as economics, statistical physics, queuing theory, biology, theoretical neurobiology, and reliability theory. Various contributions dealing with theoretical issues on stochastic processes are also included.
fusion estimation  sensor networks  random parameter matrices  multiplicative noises  random delays  realized volatility  forecast combinations  structural breaks  arithmetic progressions  first Chebyshev function  products of primes  regularly varying functions  slowly varying functions  mixed Gaussian process  small deviations  exact asymptotics  loan interest rate regulation  diffusion model  first passage time (FPT)  continuoustime Markov chains  catastrophes  bounds  birthdeath process  rate of convergence  doubleended queues  timenonhomogeneous birthdeath processes  catastrophes  repairs  transient probabilities  periodic intensity functions  timenonhomogeneous jumpdiffusion processes  transition densities  firstpassagetime  lognormal diffusion process  exogenous factors  growth curves  maximum likelihood estimation  asymptotic distribution  firstpassage time  inverse firstpassage problem  diffusion  mixture of Gaussian laws  rate of convergence  total variation distance  Wasserstein distance  weighted quadratic variation  nonMarkovian queue  general bulk service  multiple vacation  breakdown and repair  standby server  reservice  discrete time stochastic model  firstpassage time  time between inspections  hostparasite interaction  nematode infection  nonhomogeneous Poisson process  seasonal environment  Strang–Marchuk splitting approach  Cohen and Grossberg neural networks  random impulses  mean square stability  fractional differentialdifference equations  fractional queues  fractional birthdeath processes  busy period  twodimensional signature  multistate network  totally positive of order 2  stochastic order  stochastic process  reliability  stochastic orders  scale family of distributions  proportional hazard rates  differential entropy
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The aim of this special issue is to publish original research papers that cover recent advances in the theory and application of stochastic processes. There is especial focus on applications of stochastic processes as models of dynamic phenomena in various research areas, such as queuing theory, physics, biology, economics, medicine, reliability theory, and financial mathematics. Potential topics include, but are not limited to: Markov chains and processes; large deviations and limit theorems; random motions; stochastic biological model; reliability, availability, maintenance, inspection; queueing models; queueing network models; computational methods for stochastic models; applications to risk theory, insurance and mathematical finance.
measure of information  cumulative inaccuracy  mutual information  lower record values  parabolic equation  Cauchy problem  Monte Carlo method  unbiased estimator  vonNeumann–Ulam scheme  compound poisson insurance risk model  expected discounted penalty function  estimation  Fourier transform  Fouriercosine series  multidimensional birthdeath process  inhomogeneous continuoustime Markov chain  rate of convergence  one dimensional projection  Wiener–Poisson risk model  survival probability  Nonparametric threshold estimation  wet periods  total precipitation volume  asymptotic approximation  extreme order statistics  random sample size  testing statistical hypotheses  queueing systems  rate of convergence  nonstationary  Markovian queueing models  limiting characteristics  queuing network  retrials  statedependent marked Markovian arrival process  wireless telecommunication networks  timedependent queuelength probability  discretetime Geo/D/1 queue  closedform solution  Monte Carlo method  quasiMonte Carlo method  KoksmaHlawka inequality  quasirandom sequences  stochastic processes  processor heating and cooling  markovian arrival process  phasetype service time distribution  impatience  QuasiBirthandDeath process  matrixgeometric solution  truncated distribution  Markovian arrival process  multiclass arrival processes  product form  equitylinked death benefits  Fourier cosine series expansion  guaranteed minimum death benefit  option  valuation  Lévy process  compound Poisson risk model  generalized Gerber–Shiu discounted penalty function  Laplace transform  Dickson–Hipp operator  recursive formula
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Solving nonlinear equations in Banach spaces (real or complex nonlinear equations, nonlinear systems, and nonlinear matrix equations, among others), is a nontrivial task that involves many areas of science and technology. Usually the solution is not directly affordable and require an approach using iterative algorithms. This Special Issue focuses mainly on the design, analysis of convergence, and stability of new schemes for solving nonlinear problems and their application to practical problems. Included papers study the following topics: Methods for finding simple or multiple roots either with or without derivatives, iterative methods for approximating different generalized inverses, real or complex dynamics associated to the rational functions resulting from the application of an iterative method on a polynomial. Additionally, the analysis of the convergence has been carried out by means of different sufficient conditions assuring the local, semilocal, or global convergence. This Special issue has allowed us to present the latest research results in the area of iterative processes for solving nonlinear equations as well as systems and matrix equations. In addition to the theoretical papers, several manuscripts on signal processing, nonlinear integral equations, or partial differential equations, reveal the connection between iterative methods and other branches of science and engineering.
point projection  intersection  parametric curve  ndimensional Euclidean space  Newton’s second order method  fixed point theorem  nonlinear equations  multiple zeros  optimal iterative methods  higher order of convergence  nonlinear operator equation  Fréchet derivative  ?continuity condition  Newtonlike method  Frédholm integral equation  nonlinear equations  Padé approximation  iterative method  order of convergence  numerical experiment  fourth order iterative methods  local convergence  banach space  radius of convergence  nonlinear equation  iterative process  nondifferentiable operator  Lipschitz condition  high order  sixteenth order convergence method  local convergence  dynamics  Banach space  Newton’s method  semilocal convergence  Kantorovich hypothesis  iterative methods  Steffensen’s method  Rorder  with memory  computational efficiency  nonlinear equation  basins of attraction  optimal order  higher order method  computational order of convergence  nonlinear equations  multiple roots  Chebyshev–Halleytype  optimal iterative methods  efficiency index  Banach space  semilocal convergence  ?continuity condition  Jarratt method  error bound  Fredholm integral equation  Newton’s method  global convergence  variational inequality problem  split variational inclusion problem  multivalued quasinonexpasive mappings  Hilbert space  sixteenthorder optimal convergence  multipleroot finder  asymptotic error constant  weight function  purely imaginary extraneous fixed point  attractor basin  drazin inverse  generalized inverse  iterative methods  higher order  efficiency index  integral equation  efficiency index  nonlinear models  iterative methods  higher order  nonlinear equations  optimal iterative methods  multiple roots  efficiency index  iterative methods  nonlinear equations  Newtontype methods  smooth and nonsmooth operators  heston model  Hull–White  option pricing  PDE  finite difference (FD)  iteration scheme  Moore–Penrose  rectangular matrices  rate of convergence  efficiency index  nonlinear equations  conjugate gradient method  projection method  convex constraints  signal and image processing  nonlinear monotone equations  conjugate gradient method  projection method  signal processing  nonlinear systems  multipoint iterative methods  divided difference operator  order of convergence  Newton’s method  computational efficiency index  system of nonlinear equations  Newton method  NewtonHSS method  nonlinear HSSlike method  PicardHSS method  convexity  least square problem  accretive operators  signal processing  point projection  intersection  planar algebraic curve  Newton’s iterative method  the improved curvature circle algorithm  systems of nonlinear equations  King’s family  order of convergence  multipoint iterative methods  nonlinear equations  Potra–Pták method  optimal methods  weight function  basin of attraction  engineering applications  Kung–Traub conjecture  multipoint iterations  nonlinear equation  optimal order  basins of attraction
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