Dispersive Optical Solitons with Differential Group Delay Having Multiplicative White Noise by Itô Calculus by Elsayed M. E. Zayed, Mohamed E. M. Alngar, Reham M. A. Shohib, Anjan Biswas, Yakup Yıldırım, Luminita Moraru, Simona Moldovanu, Puiu Lucian Georgescu

“…The current paper recovers dispersive optical solitons in birefringent fibers that are modeled by the Schrödinger–Hirota equation with differential group delay and white noise. Itô Calculus conducts the preliminary analysis. The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfenced separators="" open="(" close=")"><msup><mi>G</mi><mo>′</mo></msup><mo>/</mo><mi>G</mi></mfenced></semantics></math></inline-formula>-expansion approach and the enhanced Kudryashov’s scheme gave way to a wide spectrum of soliton solutions with the white noise component reflected in the phase of the soliton.…”
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Stochastic Solitons in Birefringent Fibers for Biswas–Arshed Equation with Multiplicative White Noise via Itô Calculus by Modified Extended Mapping Method by Yazid Alhojilan, Hamdy M. Ahmed, Wafaa B. Rabie

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Dispersive Optical Solitons to Stochastic Resonant NLSE with Both Spatio-Temporal and Inter-Modal Dispersions Having Multiplicative White Noise by Elsayed M. E. Zayed, Mohamed E. M. Alngar, Reham M. A. Shohib

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Bifurcation studies, chaotic pattern, phase diagrams and multiple optical solitons for the (2+1)-dimensional stochastic coupled nonlinear Schrödinger system with multiplicative white noise via Itô calculus by Lu Tang

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A Spectral Method Approach to Quadratic Normal Volatility Diffusions by Peter Kink

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Stochastic Dynamics of Tumor-Immune System: A Numerical Approach by Nurgül Gökgöz

Subjects: “…itô calculus…”
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Construction of special soliton solutions to the stochastic Riccati equation by Navickas Zenonas, Timofejeva Inga, Telksnys Tadas, Marcinkevicius Romas, Ragulskis Minvydas

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Finitely additive functions in measure theory and applications by Daniel Alpay, Palle Jorgensen

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State and Control Path-Dependent Stochastic Zero-Sum Differential Games: Viscosity Solutions of Path-Dependent Hamilton–Jacobi–Isaacs Equations by Jun Moon

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Determining the background driving process of the Ornstein-Uhlenbeck model by Maria C. Mariani, Peter K. Asante, William Kubin, Osei K. Tweneboah, Maria Beccar-Varela

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Rough analysis and stochastic partial differential equations by Jin, R

“…Rama Cont,we extend the Itô calculus to paths with finite <em>p</em>-variation, where <em>p</em> is any positive real number. …”

A simple stochastic model describing the evolution of genomic GC content in asexually reproducing organisms by Jon Bohlin

“…Last, a connection between the presented model and the classical Luria–Delbrück mutation model is presented in an Itô calculus setting.…”
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Covariant nonequilibrium thermodynamics from Ito-Langevin dynamics by Mingnan Ding, Xiangjun Xing

“…The theory is based on Ito calculus, and is fully covariant under time-independent nonlinear transformation of variables. …”
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Causal functional calculus by Henry Chiu, Rama Cont

“…For paths that possess finite quadratic variation, our approach extends the Föllmer–Ito calculus and removes previous restriction on the time partition sequence. …”

Supermodular comparison inequalities in option pricing and information inequalities by Kizildemir, Bunyamin

“…Lastly, we calculate the entropy and mutual information of multidimensional Brownian motion and Poisson process by using Ito calculus and then we derive some comparison results.…”
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A transfer principle for branched rough paths by Ferrucci, E

“…These results extend previous work on 3 > p-rough paths [ABCF22], itself a generalisation of the Itô calculus on manifolds developed by Schwartz, Meyer and Émery [Sch82, Mey81, É89, É90], to the setting of non-geometric rough calculus of arbitrarily low regularity…”

Study of optical stochastic solitons of Biswas-Arshed equation with multiplicative noise by Hamood Ur Rehman, Aziz Ullah Awan, Sayed M. Eldin, Ifrah Iqbal

“…This objective of this paper is to construct stochastic solitons of Biswas-Arshed equation (BAE) under the influence of multiplicative white noise in the terms of the Itô calculus. Bright, singular, dark, periodic, singular and combined singular-dark stochastic solitons are attained by using the Sardar subequation method. …”
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Spectral theory of fluctuations in time-average statistical mechanics of reversible and driven systems by Alessio Lapolla, David Hartich, Aljaž Godec

“…Feynman-Kac formulas are rederived using Itô calculus and combined with non-Hermitian perturbation theory. …”
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Dynamics of novel exact soliton solutions to Stochastic Chiral Nonlinear Schrödinger Equation by Shafqat Ur Rehman, Jamshad Ahmad, Taseer Muhammad

“…This study enhances the theory of Itô calculus by directly performing it into analytical approaches for the solution of differential equations. …”
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Construction of analytical solutions to systems of two stochastic differential equations by Navickas Zenonas, Telksniene Inga, Telksnys Tadas, Marcinkevicius Romas, Ragulskis Minvydas

“…A scheme for the stochastization of systems of ordinary differential equations (ODEs) based on Itô calculus is presented in this article. Using the presented techniques, a system of stochastic differential equations (SDEs) can be constructed in such a way that eliminating the stochastic component yields the original system of ODEs. …”
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