Poisson sphere counting processes with random radii by Privault, Nicolas

“…The main results rely on moment formulas for Poisson stochastic integrals with random integrands.…”
Get full text
Get full text

Stein approximation for functionals of independent random sequences by Privault, Nicolas, Serafin, Grzegorz

“…We also apply this method to multiple stochastic integrals that can be used to represent U-statistics, and include linear and quadratic functionals as particular cases.…”
Get full text
Get full text

Test for cointegration rank in general vector autoregressions. by Nielsen, B

“…To prove the results the convergence of stochastic integrals with respect to singular explosive processes is considered.…”

Moments of Markovian growth-collapse processes by Privault, Nicolas

“…We apply general moment identities for Poisson stochastic integrals with random integrands to the computation of the moments of Markovian growth-collapse processes. …”
Get full text

A model for a large investor trading at market indifference prices. II: Continuous-time case by Bank, P, Kramkov, D

“…We first consider the case of simple strategies and then, in analogy to the construction of stochastic integrals, investigate the transition to general continuous dynamics. …”

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. …”

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. …”
Get full text

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. …”
Get full text

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.…”

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. …”
Get full text

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). …”
Get full text

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. …”

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. …”

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. …”
Get full text

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. …”
Get full text

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. …”
Get full text

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. …”
Get full text