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Автор: Grafiati

Опубліковано: 1 червня 2024

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Статті в журналах з теми "Stochastic calculus via regularization":

1

Platen, Eckhard, and Rolando Rebolledo. "Pricing via anticipative stochastic calculus." Advances in Applied Probability 26, no. 4 (December 1994): 1006–21. http://dx.doi.org/10.2307/1427902.

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Анотація:

The paper proposes a general model for pricing of derivative securities. The underlying dynamics follows stochastic equations involving anticipative stochastic integrals. These equations are solved explicitly and structural properties of solutions are studied.

2

Platen, Eckhard, and Rolando Rebolledo. "Pricing via anticipative stochastic calculus." Advances in Applied Probability 26, no. 04 (December 1994): 1006–21. http://dx.doi.org/10.1017/s0001867800026732.

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The paper proposes a general model for pricing of derivative securities. The underlying dynamics follows stochastic equations involving anticipative stochastic integrals. These equations are solved explicitly and structural properties of solutions are studied.

3

Atsuji, A. "Nevanlinna Theory via Stochastic Calculus." Journal of Functional Analysis 132, no. 2 (September 1995): 473–510. http://dx.doi.org/10.1006/jfan.1995.1112.

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4

Cohen, Paula, Robin Hudson, K. Parthasarathy, and Sylvia Pulmannová. "Hall's transformation via quantum stochastic calculus." Banach Center Publications 43, no. 1 (1998): 147–55. http://dx.doi.org/10.4064/-43-1-147-155.

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5

Cosso, Andrea, and Francesco Russo. "Functional Itô versus Banach space stochastic calculus and strict solutions of semilinear path-dependent equations." Infinite Dimensional Analysis, Quantum Probability and Related Topics 19, no. 04 (December 2016): 1650024. http://dx.doi.org/10.1142/s0219025716500247.

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Functional Itô calculus was introduced in order to expand a functional [Formula: see text] depending on time [Formula: see text], past and present values of the process [Formula: see text]. Another possibility to expand [Formula: see text] consists in considering the path [Formula: see text] as an element of the Banach space of continuous functions on [Formula: see text] and to use Banach space stochastic calculus. The aim of this paper is threefold. (1) To reformulate functional Itô calculus, separating time and past, making use of the regularization procedures which match more naturally the notion of horizontal derivative which is one of the tools of that calculus. (2) To exploit this reformulation in order to discuss the (not obvious) relation between the functional and the Banach space approaches. (3) To study existence and uniqueness of smooth solutions to path-dependent partial differential equations which naturally arise in the study of functional Itô calculus. More precisely, we study a path-dependent equation of Kolmogorov type which is related to the window process of the solution to an Itô stochastic differential equation with path-dependent coefficients. We also study a semilinear version of that equation.

6

Barchielli, A., and A. S. Holevo. "Constructing quantum measurement processes via classical stochastic calculus." Stochastic Processes and their Applications 58, no. 2 (August 1995): 293–317. http://dx.doi.org/10.1016/0304-4149(95)00011-u.

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7

OLIVERA, CHRISTIAN. "STOCHASTIC INTEGRATION WITH RESPECT TO THE CYLINDRICAL WIENER PROCESS VIA REGULARIZATION." Infinite Dimensional Analysis, Quantum Probability and Related Topics 16, no. 03 (September 2013): 1350024. http://dx.doi.org/10.1142/s0219025713500240.

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Following the ideas of F. Russo and P. Vallois, we use the notion of forward integral to introduce a new stochastic integral respect to the cylindrical Wiener process. This integral is an extension of the classical integral. As an application, we prove existence of solution of a parabolic stochastic differential partial equation with anticipating stochastic initial date.

8

Meyer-Brandis, Thilo, Bernt Øksendal, and Xun Yu Zhou. "A mean-field stochastic maximum principle via Malliavin calculus." Stochastics 84, no. 5-6 (February 10, 2012): 643–66. http://dx.doi.org/10.1080/17442508.2011.651619.

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9

Pamen, O. Menoukeu, F. Proske, and H. Binti Salleh. "Stochastic Differential Games in Insider Markets via Malliavin Calculus." Journal of Optimization Theory and Applications 160, no. 1 (April 19, 2013): 302–43. http://dx.doi.org/10.1007/s10957-013-0310-z.

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10

Flandoli, Franco, and Ciprian A. Tudor. "Brownian and fractional Brownian stochastic currents via Malliavin calculus." Journal of Functional Analysis 258, no. 1 (January 2010): 279–306. http://dx.doi.org/10.1016/j.jfa.2009.05.001.

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Дисертації з теми "Stochastic calculus via regularization":

1

Di, Girolami Cristina. "Infinite dimensional stochastic calculus via regularization with financial perspectives." Paris 13, 2010. http://www.theses.fr/2010PA132007.

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Ce document de thèse développe certains aspects du calcul stochastique via régularisation pour des processus X à valeurs dans un espace de Banach général B. Il introduit un concept original de -variation quadratique, où  est un sous-espace du dual d'un produit tensioriel B  B, muni de la topologie projective. Une attention particulière est dévouée au cas où B est l'espace des fonctions continues sur [-, 0],  > 0. Une classe de résultats de stabilité de classe C1 pour des processus ayant une -variation quadratique est établie ainsi que des formules d'Itô pour de tels processus. Un rôle significatif est joué par les processus réels à variation quadratique finie X (par exemple un processus de Dirichlet, faible Dirichlet). Le processus naturel à valeurs dans C [ -, 0] est le dénommé processus fenêtre Xt(. )où Xt(y)= Xt+y, y∈[-, 0]. Soit T > 0. Si X est un processus dont la variation quadratique vaut [X]t = t et h = H (XT(. )) où H : C([ -T, 0])  ℝ est une fonction de classe C3 Fréchet par rapport à L2([ -T, 0] ou H dépend d'un numéro fini d'intégrales de Wiener, il est possible de représenter h comme un nombre réel H0 plus une intégrale progressive du type ∫0T d – X où  est un processus donné explicitement. Ce résultat de représentation de la variable aléatoire h sera lié strictement à une fonction u : [0,T] x C([ -T; 0])  ℝ qui en géneral est une solution d'une équation aux dérivées partielles en dimension infinie ayant la propriété H0 = u(0, X0(. )), t = D° u(t,Xt(. )):= Dut,Xt(. ))({0}). A certains égards, ceci généralise la formule de Clark-Ocone valable lorsque X est un mouvement brownien standard W. Une des motivations vient de la théorie de la couverture d'options lorsque le prix de l'actif sous-jacent n'est pas une semimartingale
This thesis develops some aspects of stochastic calculus via regularization to Banach valued processes. An original concept of -quadratic variation is introduced, where  is a subspace of the dual of a tensor product B  B where B is the values space of some process X process. Particular interest is devoted to the case when B is the space of real continuous functions defined on [-, 0], > 0. Itô formulae and stability of finite -quadratic variation processes are established. Attention is deserved to a finite real quadratic variation (for instance Dirichlet, weak Dirichlet) process X. The C [ -, 0] -valued process X(. ) defined by Xt(y)= Xt+y, where y∈[-, 0], is called window process. Let T > 0. If X is a finite quadratic variation process such that [X]t = t and h = H (XT(. )) où H : C([ -T, 0])  ℝ is L2([ -T, 0]-smooth or H non smooth but finitely based it is possible to represent h as a sum of a real H0 plus a forward integral of type ∫0T d – X où H0 et  are explicitly given. This representation result will be strictly linked with a function u : [0,T] x C([ -T; 0])  ℝ which in general solves an infinite dimensional partial differential equation with the property H0 = u(0, X0(. )), t = D° u(t,Xt(. )):= Dut,Xt(. ))({0}). This decomposition generalizes important aspects of Clark-Ocone formula which is true when X is the standard Brownian motion W. The financial perspective of this work is related to hedging theory of path dependent options without semimartingales

2

DI, GIROLAMI CRISTINA. "Infinite dimensional stochastic calculus via regularization with financial motivations." Doctoral thesis, Luiss Guido Carli, 2010. http://hdl.handle.net/11385/200841.

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Calculus via regularization. [chi]-quadratic variation. Evaluations of [chi]-quadratic variations. Stability of [chi]-quadratic variation and of [chi]-covariation. Ito's formula. A generalized Clark-Ocone formula.

3

Teixeira, Nicácio De Messias Alan. "Stochastic Analysis of non-Markovian irregular phenomena." Electronic Thesis or Diss., Institut polytechnique de Paris, 2022. http://www.theses.fr/2022IPPAE006.

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Cette thèse se concentre sur certains aspects d'analyse stochastique de modèles non-markoviens irréguliers. On formule existence et unicité pour certains problèmes de martingales impliquant deux types de dérive irrégulière perturbée par des fonctionnelles dépendant de la trajectoire. Dans le premier cas, on considère le cas où la dérive est la dérivée d'une fonction continue: le modèle correspondant est celui de milieux aléatoires irréguliers dépendant de la trajectoire. Le second concerne le cas où la dérive est celui d'un processus de Bessel en basse dimension: dans ce cas il est bien connu qu'en général les processus ne sont pas des semimartingales. Enfin la thèse explore également des relations et des analogies entre la théorie des chemins rugueux et le calcul stochastique via régularisation
This thesis focuses on some particular stochastic analysis aspects of non-Markovian irregular phenomena. It formulates existence and uniqueness for some martingale problems involving two types of irregulat drifts perturbed by path-dependant functionals: the first one is related to the case which is the derivative of continuous function and it models irregular path-dependent media; the second one concerns the case when the drift is of Bessel type in low dimension. Finally the thesis also focuses on rough paths techniques and its relation with the stochastic calculus via regularization

4

Ashu, Tom A. Ashu. "Non-Smooth SDEs and Hyperbolic Lattice SPDEs Expansions via the Quadratic Covariation Differentiation Theory and Applications." Kent State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=kent1500334062680747.

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Книги з теми "Stochastic calculus via regularization":

1

Russo, Francesco, and Pierre Vallois. Stochastic Calculus via Regularizations. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-09446-0.

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2

Vallois, Pierre, and Francesco Russo. Stochastic Calculus Via Regularizations. Springer International Publishing AG, 2022.

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3

Guionnet, Alice. Free probability. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.003.0003.

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Free probability was introduced by D. Voiculescu as a theory of noncommutative random variables (similar to integration theory) equipped with a notion of freeness very similar to independence. In fact, it is possible in this framework to define the natural ‘free’ counterpart of the central limit theorem, Gaussian distribution, Brownian motion, stochastic differential calculus, entropy, etc. It also appears as the natural setup for studying large random matrices as their size goes to infinity and hence is central in the study of random matrices as their size go to infinity. In this chapter the free probability framework is introduced, and it is shown how it naturally shows up in the random matrices asymptotics via the so-called ‘asymptotic freeness’. The connection with combinatorics and the enumeration of planar maps, including loop models, are discussed.

Частини книг з теми "Stochastic calculus via regularization":

1

Russo, Francesco, and Pierre Vallois. "Stochastic Integration via Regularization." In Stochastic Calculus via Regularizations, 113–64. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-09446-0_4.

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2

Russo, Francesco, and Pierre Vallois. "Calculus via Regularization and Rough Paths." In Stochastic Calculus via Regularizations, 597–615. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-09446-0_17.

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3

Russo, Francesco, and Pierre Vallois. "Elements of Wiener Analysis." In Stochastic Calculus via Regularizations, 333–71. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-09446-0_10.

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4

Russo, Francesco, and Pierre Vallois. "Stochastic Calculus with n-Covariations." In Stochastic Calculus via Regularizations, 557–96. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-09446-0_16.

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5

Russo, Francesco, and Pierre Vallois. "Stability of the Covariation and Itô’s Formula." In Stochastic Calculus via Regularizations, 199–232. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-09446-0_6.

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6

Russo, Francesco, and Pierre Vallois. "Itô Integrals." In Stochastic Calculus via Regularizations, 165–98. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-09446-0_5.

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7

Russo, Francesco, and Pierre Vallois. "Weak Dirichlet Processes." In Stochastic Calculus via Regularizations, 531–55. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-09446-0_15.

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8

Russo, Francesco, and Pierre Vallois. "Itô SDEs with Non-Lipschitz Coefficients." In Stochastic Calculus via Regularizations, 445–89. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-09446-0_13.

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9

Russo, Francesco, and Pierre Vallois. "Hermite Polynomials and Wiener Chaos Expansion." In Stochastic Calculus via Regularizations, 309–32. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-09446-0_9.

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10

Russo, Francesco, and Pierre Vallois. "Change of Probability and Martingale Representation." In Stochastic Calculus via Regularizations, 233–57. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-09446-0_7.

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Тези доповідей конференцій з теми "Stochastic calculus via regularization":

1

Zheng, Jun, Li Yu, and Peng Yang. "Throughput analysis of cognitive radio networks via stochastic network calculus." In 2014 Sixth International Conference on Wireless Communications and Signal Processing (WCSP). IEEE, 2014. http://dx.doi.org/10.1109/wcsp.2014.6992170.

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2

Lecca, P., C. Priami, C. Laudanna та G. Constantin. "Predicting cell adhesion probability via the biochemical stochastic π-calculus". У the 2004 ACM symposium. New York, New York, USA: ACM Press, 2004. http://dx.doi.org/10.1145/967900.967944.

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3

Guan, Yue, Qifan Zhang, and Panagiotis Tsiotras. "Learning Nash Equilibria in Zero-Sum Stochastic Games via Entropy-Regularized Policy Approximation." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/339.

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We explore the use of policy approximations to reduce the computational cost of learning Nash equilibria in zero-sum stochastic games. We propose a new Q-learning type algorithm that uses a sequence of entropy-regularized soft policies to approximate the Nash policy during the Q-function updates. We prove that under certain conditions, by updating the entropy regularization, the algorithm converges to a Nash equilibrium. We also demonstrate the proposed algorithm's ability to transfer previous training experiences, enabling the agents to adapt quickly to new environments. We provide a dynamic hyper-parameter scheduling scheme to further expedite convergence. Empirical results applied to a number of stochastic games verify that the proposed algorithm converges to the Nash equilibrium, while exhibiting a major speed-up over existing algorithms.

4

Priezzhev, Ivan, Dmitry Danko, and Uwe Strecker. "New-Age Kolmogorov Full-Function Neural Network KNN Offers High-Fidelity Reservoir Predictions via Estimation of Core, Well Log, Map and Seismic Properties." In Abu Dhabi International Petroleum Exhibition & Conference. SPE, 2021. http://dx.doi.org/10.2118/207575-ms.

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Abstract Instead of relying on analytical functions to approximate property relationships, this innovative hybrid neural network technique offers highly adaptive, full-function (!) predictions that can be applied to different subsurface data types ranging from (1.) core-to-log prediction (permeability), (2.) multivariate property maps (oil-saturated thickness maps), and, (3.) petrophysical properties from 3D seismic data (i.e., hydrocarbon pore volume, instantaneous velocity). For each scenario a separate example is shown. In case study 1, core measurements are used as the target array and well log data serve training. To analyze the uncertainty of predicted estimates, a second oilfield case study applies 100 iterations of log data from 350 wells to obtain P10-P50-P90 probabilities by randomly removing 40% (140 wells) for validation purposes. In a third case study elastic logs and a low-frequency model are used to predict seismic properties. KNN generates a high level of freedom operator with only one (or more) hidden layer(s). Iterative parameterization precludes that high correlation coefficients arise from overtraining. Because the key advantage of the Kolmogorov neural network (KNN) is to permit non-linear, full-function approximations of reservoir properties, the KNN approach provides a higher-fidelity solution in comparison to other linear or non-linear neural net regressions. KNN offers a fast-track alternative to classic reservoir property predictions from model-based seismic inversions by combining (a) Kolmogorov's Superposition Theorem and (b) principles of genetic inversion (Darwin's "Survival of the fittest") together with Tikhonov regularization and gradient theory. In practice, this is accomplished by minimizing an objective function on multiple and simultaneous outputs from full-function (via look-up table) Kolmogorov neural network runs. All case studies produce high correlations between actual and predicted properties when compared to other stochastic or deterministic inversions. For instance, in the log to seismic prediction better (simulated) resolution of neural network results can be discerned compared to traditional inversion results. Moreover, all blind tests match the overall shape of prominent log curve deflections with a higher degree of fidelity than from inversion. An important fringe benefit of KNN application is the observed increase in seismic resolution that by comparison falls between the seismic resolution of a model-based inversion and the simulated resolution from seismic stochastic inversion.