Pathwise integration with respect to paths of finite quadratic variation by Ananova, A, Cont, R

“…We show that the integral satisfies a pathwise isometry property, analogous to the well-known Ito isometry for stochastic integrals. This property is then used to represent the integral as a continuous map on an appropriately defined vector space of integrands. …”

A stochastic differential equation model for pest management by Xuewen Tan, Sanyi Tang, Xiaozhou Chen, Lianglin Xiong, Xinzhi Liu

“…Abstract In order to comprehend the effects of the duration of pesticide residual effectiveness on successful pest control, a stochastic integrated pest management (IPM) model with pesticides which have residual effects is proposed. …”
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Normal approximation of compound Hawkes functionals by Khabou, Mahmoud, Privault, Nicolas, Réveillac, Anthony

“…We derive quantitative bounds in the Wasserstein distance for the approximation of stochastic integrals with respect to Hawkes processes by a normally distributed random variable. …”
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Existence of Lévy's area and pathwise integration by Imkeller, P, Prömel, D

“…For two paths, one of which is controlled by the other, a pathwise construction of the L´evy area and therefore of mutual stochastic integrals is possible. If the existence of quadratic variation along a sequence of partitions is guaranteed, this leads us to a study of the pathwise change of variable (Itˆo) formula in the spirit of F¨ollmer, from the perspective of controlled paths. …”

Moments of quantum Lévy areas using sticky shuffle Hopf algebras by Hudson, R, Schauz, U, Wu, Y

“…They are defined as second rank iterated stochastic integrals against the components of planar Brownian motion, which are one-dimensional Brownian motions satisfying Heisenberg-type commutation relations. …”

Stochastic analysis, rough path analysis and fractional Brownian motions by Coutin, L, Qian, Z

“…By the results in [Ly1], a stochastic integration theory may be established for fractional Brownian motions, and strong solutions and a Wong-Zakai type limit theorem for stochastic differential equations driven by fractional Brownian motions can be deduced accordingly. …”

Guaranteed Bounds on Information-Theoretic Measures of Univariate Mixtures Using Piecewise Log-Sum-Exp Inequalities by Frank Nielsen, Ke Sun

“…Since the Kullback–Leibler divergence of mixtures provably does not admit a closed-form formula, it is in practice either estimated using costly Monte Carlo stochastic integration, approximated or bounded using various techniques. …”
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Areas of areas generate the shuffle algebra by Diehl, J, Lyons, T, Preiß, R, Reizenstein, J

“…We finally discuss compatibility between the area operator and discrete integration and stochastic integration and conclude with some results on the linear span of the areas of areas.…”

A sampling theory for infinite weighted graphs by Palle E. T. Jorgensen

“…We will solve this problem with the use of ideas from stochastic integration.…”
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Renormalization Group Method for a Stochastic Differential Equation with Multiplicative Fractional White Noise by Lihong Guo

“…The driving process is a real-valued fractional white noise with a Hurst parameter greater than <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula>. The stochastic integration is understood in the Wick–Itô–Skorohod sense. …”
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Physics of psychophysics: Large dynamic range in critical square lattices of spiking neurons by Emilio F. Galera, Osame Kinouchi

“…Here we examine a sensory epithelium composed of two connected square lattices of stochastic integrate-and-fire cells. With one square lattice, we obtain a Stevens's law ρ∝h^{m} with Stevens's exponent m=0.254 and a sigmoidal saturation, where ρ is the neuronal network activity and h is the input intensity (external field). …”
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Quantum omega-semimartingales and stochastic evolutions by Belton, A

“…It is shown that the (non-adapted) quantum stochastic integrals of bounded, <em>omega</em>-adapted processes are themselves bounded and <em>omega</em>-adapted, a fact that may be deduced from the Bismut–Clark–Ocone formula of Malliavin calculus. …”

Robust Student&#x2019;s t-Based Stochastic Cubature Filter for Nonlinear Systems With Heavy-Tailed Process and Measurement Noises by Yulong Huang, Yonggang Zhang

“…The existing stochastic integration rule is a special case of the proposed SSTSRCR when the degrees of freedom parameter tends to infinity. …”
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Weakly nonlinear response of noisy neurons by Sergej O Voronenko, Benjamin Lindner

“…We calculate the instantaneous firing rate of a stochastic integrate-and-fire neuron driven by an arbitrary time-dependent signal up to second order in the signal amplitude. …”
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An extension of the stochastic sewing lemma and applications to fractional stochastic calculus by Toyomu Matsuda, Nicolas Perkowski

“…The first is to prove the convergence of Itô or Stratonovich approximations of stochastic integrals along fractional Brownian motions under low regularity assumptions. …”
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Parameter Estimation for Additive Hazard Model Recurrent Event Using Counting Process Approach by Wuryandari, Triastuti, Gunardi, Gunardi, Danardono, Danardono

“…The counting process approach was first developed by Aalen on 1975 which combines elements of stochastic integration, martingale theory and counting process theory. …”
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Stochastic control for linear systems driven by fractional noises by Yaozhong, H, Zhou, X

“…First, as a prerequisite for studying the underlying control problems, some new results on stochastic integrals and stochastic differential equations associated with FBM are established. …”

Stochastic lattice-based modelling of malaria dynamics by Phong V. V. Le, Praveen Kumar, Marilyn O. Ruiz

“…The It$$\hat{o}$$ o^ approximation of stochastic integrals with respect to Brownian motion was used to derive a model of stochastic differential equations. …”
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Space-Time Inversion of Stochastic Dynamics by Massimiliano Giona, Antonio Brasiello, Alessandra Adrover

“…The mathematical interpretation of the resulting Fokker-Planck equation can be obtained by introducing a new way of considering the stochastic integrals over the increments of a Wiener process, referred to as stochastic Stjelties integrals of mixed order. …”
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A stochastic joint model for longitudinal and survival data with cure patients by Abu Bakar, Mohd Rizam, A. Salah, Khalid, Ibrahim, Noor Akma, Haron, Kassim

“…For the longitudinal model, a stochastic Integrated Ornstein-Uhlenbeck process will be presented. …”
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