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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Nonlinear Stochastic Equation within an Itô Prescription for Modelling of Financial Market by Leonardo S. Lima

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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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Instantaneous Frequency Estimation Using Stochastic Calculus and Bootstrapping by Abutaleb A

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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. …”

The backward Îto method for the Lagrangian simulation of transport processes with large space variations of the diffusivity by D. Spivakovskaya, A. W. Heemink, E. Deleersnijder

“…The random walk model based on backward Îto calculus can be used for these problems. This model was proposed by LaBolle et al. (2000). …”
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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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