Relevant bibliographies by topics / Itô's integral

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Itô's integral'

Author: Grafiati
Published: 4 June 2021
Last updated: 12 February 2022

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Journal articles on the topic "Itô's integral"

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Chew Tuan-Seng, Tay Jing-Yi, and Toh Tin-Lam. "The Non-Uniform Riemann Approach to Itô's Integral." Real Analysis Exchange 27, no. 2 (2002): 495. http://dx.doi.org/10.14321/realanalexch.27.2.0495.

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Li, Wenxue, Meng Liu, and Ke Wang. "A Generalization of Itô's Formula and the Stability of Stochastic Volterra Integral Equations." Journal of Applied Mathematics 2012 (2012): 1–16. http://dx.doi.org/10.1155/2012/292740.

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It is well known that Itô’s formula is an essential tool in stochastic analysis. But it cannot be used for general stochastic Volterra integral equations (SVIEs). In this paper, we first introduce the concept of quasi-Itô process which is a generalization of well-known Itô process. And then we extend Itô’s formula to a more general form applicable to some kinds of SVIEs. Furthermore, the stability in probability for some SVIEs is analyzed by the generalized Itô’s formula. Our work shows that the generalized Itô’s formula is powerful and flexible to use in many relevant fields.
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Labendia, Mhelmar A., Timothy Robin Y. Teng, and Elvira P. de Lara-Tuprio. "Itô-Henstock integral and Itô's formula for the operator-valued stochastic process." Mathematica Bohemica 143, no. 2 (June 1, 2017): 135–60. http://dx.doi.org/10.21136/mb.2017.0084-16.

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Wang, Hao. "Singular Spacetime Itô's Integral and a Class of Singular Interacting Branching Particle Systems." Infinite Dimensional Analysis, Quantum Probability and Related Topics 06, no. 02 (June 2003): 321–35. http://dx.doi.org/10.1142/s0219025703001201.

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In Wang,8 a class of interacting measure-valued branching diffusions [Formula: see text] with singular coefficient were constructed and characterized as a unique solution to ℒε-martingale problem by a limiting duality method since in this case the dual process does not exist. In this paper, we prove that for any ε ≠ 0 the superprocess with singular motion coefficient is just the super-Brownian motion. The singular motion coefficient is handled as a sequential limit motivated by Antosik et al.1 Thus, the limiting superprocess is investigated and identified as the motion coefficient converges to a singular function. The representation of the singular spacetime Itô's integral is derived.
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Wang, Hao. "ADDENDUM: "SINGULAR SPACETIME ITÔ'S INTEGRAL AND A CLASS OF SINGULAR INTERACTING BRANCHING PARTICLE SYSTEMS"." Infinite Dimensional Analysis, Quantum Probability and Related Topics 07, no. 01 (March 2004): 161–62. http://dx.doi.org/10.1142/s0219025704001347.

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Wu, Jiang-Lun. "On the regularity of stochastic difference equations in hyperfinite-dimensional vector spaces and applications to -valued stochastic differential equations." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 124, no. 6 (1994): 1089–117. http://dx.doi.org/10.1017/s0308210500030134.

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Nonstandard analysis is used, in this paper, to give a construction of a Wiener -process Wt, t ∈ [0, ∞). From this, a hyperfinite representation of stochastic integrals for operatorvalued processes with respect to Wt is derived, and existence theorems in the spirit of Keisler are proved for (infinite-dimensional) stochastic differential equations of Itô's type one and a certain kind of Itô's type two, via regularity of hyperfinite stochastic difference equations.
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ES-SEBAIY, KHALIFA, and CIPRIAN A. TUDOR. "MULTIDIMENSIONAL BIFRACTIONAL BROWNIAN MOTION: ITÔ AND TANAKA FORMULAS." Stochastics and Dynamics 07, no. 03 (September 2007): 365–88. http://dx.doi.org/10.1142/s0219493707002050.

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Kachanovsky, N. A. "On extended stochastic integrals with respect to Lévy processes." Carpathian Mathematical Publications 5, no. 2 (December 30, 2013): 256–78. http://dx.doi.org/10.15330/cmp.5.2.256-278.

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Let $L$ be a Levy process on $[0,+\infty)$. In particular cases, when $L$ is a Wiener or Poisson process, any square integrable random variable can be decomposed in a series of repeated stochastic integrals from nonrandom functions with respect to $L$. This property of $L$, known as the chaotic representation property (CRP), plays a very important role in the stochastic analysis. Unfortunately, for a general Levy process the CRP does not hold. There are different generalizations of the CRP for Levy processes. In particular, under the Ito's approach one decomposes a Levy process $L$ in the sum of a Gaussian process and a stochastic integral with respect to a Poisson random measure, and then uses the CRP for both terms in order to obtain a generalized CRP for $L$. The Nualart-Schoutens's approach consists in decomposition of a square integrable random variable in a series of repeated stochastic integrals from nonrandom functions with respect to so-called orthogonalized centered power jump processes, these processes are constructed with using of a cadlag version of $L$. The Lytvynov's approach is based on orthogonalization of continuous monomials in the space of square integrable random variables. In this paper we construct the extended stochastic integral with respect to a Levy process and the Hida stochastic derivative in terms of the Lytvynov's generalization of the CRP; establish some properties of these operators; and, what is most important, show that the extended stochastic integrals, constructed with use of the above-mentioned generalizations of the CRP, coincide.
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Applebaum, David, and Michailina Siakalli. "Asymptotic Stability of Stochastic Differential Equations Driven by Lévy Noise." Journal of Applied Probability 46, no. 04 (December 2009): 1116–29. http://dx.doi.org/10.1017/s0021900200006173.

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Using key tools such as Itô's formula for general semimartingales, Kunita's moment estimates for Lévy-type stochastic integrals, and the exponential martingale inequality, we find conditions under which the solutions to the stochastic differential equations (SDEs) driven by Lévy noise are stable in probability, almost surely and moment exponentially stable.
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Applebaum, David, and Michailina Siakalli. "Asymptotic Stability of Stochastic Differential Equations Driven by Lévy Noise." Journal of Applied Probability 46, no. 4 (December 2009): 1116–29. http://dx.doi.org/10.1239/jap/1261670692.

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Using key tools such as Itô's formula for general semimartingales, Kunita's moment estimates for Lévy-type stochastic integrals, and the exponential martingale inequality, we find conditions under which the solutions to the stochastic differential equations (SDEs) driven by Lévy noise are stable in probability, almost surely and moment exponentially stable.
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Dissertations / Theses on the topic "Itô's integral"

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Bahník, Michal. "Stochastické obyčejné diferenciálni rovnice." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2015. http://www.nusl.cz/ntk/nusl-232074.

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Diplomová práce se zabývá problematikou obyčejných stochastických diferenciálních rovnic. Po souhrnu teorie stochastických procesů, zejména tzv. Brownova pohybu je zaveden stochastický Itôův integrál, diferenciál a tzv. Itôova formule. Poté je definováno řešení počáteční úlohy stochastické diferenciální rovnice a uvedena věta o existenci a jednoznačnosti řešení. Pro případ lineární rovnice je odvozen tvar řešení a rovnice pro jeho střední hodnotu a rozptzyl. Závěr tvoří rozbor vybraných rovnic.
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Niski, Fabio. "Integral estocástica e aplicações." Universidade de São Paulo, 2009. http://www.teses.usp.br/teses/disponiveis/45/45132/tde-07122009-131027/.

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O aumento pelo interesse na teoria de integração estocástica é, basicamente, consequência da acirrada competição para entender, desenvolver e aplicar a matemática subjacente ao mercado mobiliário. Neste trabalho desenvolvemos, de maneira didática e visando aplicações, tal teoria. Para tanto, começamos apresentando um desenvolvimento cuidadoso da teoria dos martingais e dos principais resultados de medida e probabilidade relacionados. Depois apresentamos de maneira formal a teoria de integração estocástica com respeito aos semi-martingais contínuos. Finalizamos com um tratamento das principais aplicações dessa teoria como a fórmula de Itô, uma introdução às equações diferenciais estocásticas e a fórmula de Feynman-Kac. Apresentamos também, em um apêndice, a teoria de mudança de medida e o teorema de Girsanov. Tentamos durante o trabalho apresentar exemplos relacionados com finanças e ilustrar a importância do movimento Browniano.
The increasing interest in the theory of Stochastic Integration is due mainly to the competitive pressure to understand, develop and apply the underlying mathematics of security markets. In this work, we attempt to develop part of the theory in a didactical approach and focused toward some particular applications. For this purpose, we begin by introducing a thorough development of Martingale theory and the main related results on Measure and Probability theory. We then present in a formal way the Stochastic Integration Theory with respect to continuous Semimartingales. Subsequentially, we show some of the theory\'s main applications, such as Itô\'s formula, an introduction to the theory of Stochastic Differential Equations and Feynman-Kac\'s formula. We also present in the appendix Girsanov\'s theorem and a construction of Brownian motion. During the development of this text we endeavored to enrich it by including examples relevant to finance and emphasizing the importance of the ubiquitous Brownian motion.
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Misturini, Ricardo. "Movimento browniano, integral de Itô e introdução às equações diferenciais estocásticas." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2010. http://hdl.handle.net/10183/24926.

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Este texto apresenta alguns dos elementos básicos envolvidos em um estudo introdutório das equações diferencias estocásticas. Tais equações modelam problemas a tempo contínuo em que as grandezas de interesse estão sujeitas a certos tipos de perturbações aleatórias. Em nosso estudo, a aleatoriedade nessas equações será representada por um termo que envolve o processo estocástico conhecido como Movimento Browniano. Para um tratamento matematicamente rigoroso dessas equações, faremos uso da Integral Estocástica de Itô. A construção dessa integral é um dos principais objetivos do texto. Depois de desenvolver os conceitos necessários, apresentaremos alguns exemplos e provaremos existência e unicidade de solução para equações diferenciais estocásticas satisfazendo certas hipóteses.
This text presents some of the basic elements involved in an introductory study of stochastic differential equations. Such equations describe certain kinds of random perturbations on continuous time models. In our study, the randomness in these equations will be represented by a term involving the stochastic process known as Brownian Motion. For a mathematically rigorous treatment of these equations, we use the Itô Stochastic Integral. The construction of this integral is one of the main goals of the text. After developing the necessary concepts, we present some examples and prove existence and uniqueness of solution of stochastic differential equations satisfying some hypothesis.
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Grunert, Sandro. "Itô’s Lemma." Universitätsbibliothek Chemnitz, 2009. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200900979.

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Itô’s Lemma Ausarbeitung im Rahmen des Seminars "Finanzmathematik", SS 2009 Die Arbeiten des japanischen Mathematikers Kiyosi Itô aus den 1940er Jahren bilden heute die Grundlage der Theorie stochastischer Integration und stochastischer Differentialgleichungen. Die Ausarbeitung beschäftigt sich mit Itô's Kalkül, in dem zunächst das Itô-Integral bezüglich diverser Integratoren bereitgestellt wird, um sich anschließend mit Itô's Lemma bzw. der Itô-Formel als grundlegendes Hilfsmittel stochastischer Integration zu widmen. Am Ende wird ein kurzer Ausblick auf das Black-Scholes-Modell für zeitstetige Finanzmärkte vollzogen. Grundlage für die Ausarbeitung ist das Buch "Risk-Neutral Valuation" von Nicholas H. Bingham und Rüdiger Kiesel.
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Johansson, Karin. "“It's not art; it's not therapy; it's something else” : an investigation into how aesthetic practice can be used in pedagogic situations for pupils to examine and reflect on themselves." Thesis, Konstfack, Institutionen för Bildpedagogik (BI), 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:konstfack:diva-3841.

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In this investigation, I discuss how students can examine and reflect on themselves through aesthetic practice in various pedagogic situations. The field study took place over two months in the international settlement of Auroville in the south of India, where I visited schools and observed various pedagogical methods. In this study, I focus on two of these pedagogical methods: Play of Painting and Awareness Through the Body. In both, the body is considered an important part of the student’s learning and development. These experiences form the background for this investigation. I investigated Play of Painting and Awareness Through the Body through focussing on one lesson from each method. I describe how the methods are organised and practised in Auroville schools with observations, visual material, and interviews from my field study.  In this investigation, I use a phenomenological and aesthetic perspective together with a brief introduction to the theory of Integral Education. I believe that aesthetics can be used in many different ways in a school context. In this thesis, I use the term aesthetic practices to understand and study Awareness Through the Body and Play of Painting. I see these methods as two examples of how aesthetic practices and conditions for aesthetic learning processes with different ways of reflection can be encouraged in an educational environment.  The children in Play of Painting and Awareness Through the Body learn about themselves through the experience of practising aesthetics with their whole bodies and senses. Through creating conditions for aesthetic practice as in Awareness Through the Body and Play of Painting, children can reflect on themselves together with others.  The purpose of this investigation is to research how aesthetic practices can be used in pedagogic situations through the methods Play of Painting and Awareness Through the Body. I focus on how pupils can examine and reflect on themselves through aesthetic practice in these two methods.
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Wang, Qingfeng. "Rough path properties for local time of symmetric alpha stable processes." Thesis, Loughborough University, 2012. https://dspace.lboro.ac.uk/2134/11052.

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Medeiros, Rogério de Assis. "Aplicações do cálculo estocástico à análise complexa." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/45/45132/tde-17052012-181529/.

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Nesta dissertação desenvolvemos o Cálculo Estocástico para provar teoremas clássicos de Análise Complexa, em particular, o pequeno teorema de Picard.
In this dissertation we develop the Stochastic Calculus for to prove classical theorems in Complex Analysis, in particular, the little Picard\'s theorem.
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Lee, Jau-Long, and 李昭龍. "The Study of Using Self-learning Expert System to Integrate Image Recognition and It's Application to a Robot Arm." Thesis, 1997. http://ndltd.ncl.edu.tw/handle/16768770663415052374.

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Books on the topic "Itô's integral"

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Back, Kerry E. Brownian Motion and Stochastic Calculus. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780190241148.003.0012.

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Brownian motion and concepts of the Itôs calculus are explained, including total variation, quadratic variation, Levy’s characterization of Brownian motion, the Itô integral, the difference between martingales and local martingales, the martingale (predictable) representation theorem , Itô’s formula (Itô’s lemma), geometric Brownian motion, covariation (joint variation) processes, the relationship between variance and expected quadratic variation, the relationship between covariance and expected covariation, and rotations of Brownian motions.
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Book chapters on the topic "Itô's integral"

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Da Prato, Giuseppe. "Itô’s integral." In Introduction to Stochastic Analysis and Malliavin Calculus, 85–104. Pisa: Scuola Normale Superiore, 2014. http://dx.doi.org/10.1007/978-88-7642-499-1_6.

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Steele, J. Michael. "Localization and Itô’s Integral." In Stochastic Calculus and Financial Applications, 95–109. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4684-9305-4_7.

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Major, Péter. "The Proof of Itô’s Formula: The Diagram Formula and Some of Its Consequences." In Multiple Wiener-Itô Integrals, 43–64. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-02642-8_5.

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Ikeda, Nobuyuki, and Shojiro Manabe. "Van Vleck-Pauli formula for Wiener integrals and Jacobi fields." In Itô’s Stochastic Calculus and Probability Theory, 141–56. Tokyo: Springer Japan, 1996. http://dx.doi.org/10.1007/978-4-431-68532-6_9.

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Cherny, A. S. "Principal Values of the Integral Functionals of Brownian Motion: Existence, Continuity and an Extension of Itô’s Formula." In Séminaire de Probabilités XXXV, 348–70. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-540-44671-2_24.

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Anand, Adarsh, Shakshi Singhal, and Ompal Singh. "Revisiting Dynamic Potential Adopter Diffusion Models under the Influence of Irregular Fluctuations in Adoption Rate." In Handbook of Research on Promoting Business Process Improvement Through Inventory Control Techniques, 499–519. IGI Global, 2018. http://dx.doi.org/10.4018/978-1-5225-3232-3.ch026.

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A pragmatic innovation diffusion model is proposed in the present chapter that interpolates stochasticity in the logistic formulation of the widely-acknowledged Bass model with dynamic market size. These irregular changes are caused due to uncertainty attached to the socioeconomic and political environment in which an innovation is positioned that affects the action of potential adopters leading to their non-uniform behavior. The aim of the current study is to find the analytical solution for the two dynamic market expansion structures, namely, linear and exponential under the influence of irregular fluctuations whose closed-form solutions were not possible in the existing literature. In addition to the changeable market size, the proposed innovation diffusion also incorporates the concept of repeat purchase. The anticipated stochastic differential equation based new product diffusion model is then expounded methodically using the Itô process and Itô's integral equation. Further, the model has been used to study the growth pattern of different consumer durable products.
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"Itô’s stochastic integral." In Translations of Mathematical Monographs, 77–139. Providence, Rhode Island: American Mathematical Society, 1994. http://dx.doi.org/10.1090/mmono/142/03.

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Balchin, Kevin, and Carol Wild. "It's All in the Numbers." In Cross-Cultural Perspectives on Technology-Enhanced Language Learning, 203–21. IGI Global, 2018. http://dx.doi.org/10.4018/978-1-5225-5463-9.ch012.

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This chapter focuses on teacher professional development and TELL, and the constraints of TELL. More specifically, it explores some of the barriers and enablers to the use of technology in English language classes in six secondary school across Malaysia, in both rural and urban settings. The cross-cultural aspect of the study comes from a comparison of the schools involved and considerations of context-appropriate technological tools and materials in the differing school environments. The backdrop to the study is the Malaysian Ministry of Education (MMoE). One particular issue highlighted in the study is the benefit of communities of teachers working together to implement and integrate technology into their teaching.
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Balchin, Kevin, and Carol Wild. "It's All in the Numbers." In TPACK, 185–203. IGI Global, 2019. http://dx.doi.org/10.4018/978-1-5225-7918-2.ch008.

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This chapter focuses on teacher professional development and TELL, and the constraints of TELL. More specifically, it explores some of the barriers and enablers to the use of technology in English language classes in six secondary school across Malaysia, in both rural and urban settings. The cross-cultural aspect of the study comes from a comparison of the schools involved and considerations of context-appropriate technological tools and materials in the differing school environments. The backdrop to the study is the Malaysian Ministry of Education (MMoE). One particular issue highlighted in the study is the benefit of communities of teachers working together to implement and integrate technology into their teaching.
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Bisen, Shilpa Suresh, and Yogesh Deshpande. "The Repercussion of the Internet on Psychological Wellbeing." In Advances in Psychology, Mental Health, and Behavioral Studies, 101–17. IGI Global, 2019. http://dx.doi.org/10.4018/978-1-5225-8449-0.ch005.

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The internet is an essential and integral part of our lives, whether it's about looking for a meaning of a word, searching for a journal, shopping, or connecting to others. Human beings cannot think of life without the internet. Although it's having a positive impact, the negative side is there. Problematic internet use is defined as non-chemical or behavioral addictions, which involve human-machine interactions and can be harmful as it leads to numerous forms of psychological disorders. The chapter addresses various psychopathologies arising due to excessive internet use (e.g., problematic internet use, online gaming, online gambling, and compulsive cybersex). The chapter frames a strong theoretical background along with recent controversial issues related to the disorder. The chapter is delineated to acquaint readers with new concepts arising in clinical psychology that will help mental health professionals to be well equipped with skills required for the prevention and treatment of internet-related psychological disorders.
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Conference papers on the topic "Itô's integral"

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Lindley, Siân E., Sam Meek, Abigail Sellen, and Richard Harper. ""It's simply integral to what I do"." In the 21st international conference. New York, New York, USA: ACM Press, 2012. http://dx.doi.org/10.1145/2187836.2187979.

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TANG, SHANJIAN. "NONCONVEXITY PHENOMENON ON ITÔ'S INTEGRALS AND ON STOCHASTIC ATTAINABLE SETS." In Control Theory and Related Topics - In Memory of Professor Xunjing Li. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812790552_0011.

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