Stochastic integration by parts and functional itô calculus by Bally, V, Caramellino, L, Cont, R

“…Rama Cont's notes provide an introduction to the Functional Itô Calculus, a non-anticipative functional calculus that extends the classical Itô calculus to path-dependent functionals of stochastic processes. …”

The Ito calculus: a vector-integral approach by Ling, PD

“…The Itô calculus is the theory of stochastic integrals ∫^t₀ X_u dS_u, where S is a semimartingale, and X is a suitable previsible process. …”

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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15.070 Advanced Stochastic Processes, Fall 2005 by Gamarnik, David, Shah, Premal

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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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Stochastic calculus and differential equations for physics and finance / by Mccauley, Joseph L

“…The book develops Ito calculus and Fokker-Planck equations as parallel approaches to stochastic processes, using those methods in a unified way. …”

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…”