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Journal articles on the topic 'Stochastic Differential Inclusions'

Author: Grafiati

Published: 23 November 2024

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1

Benaïm, Michel, Josef Hofbauer, and Sylvain Sorin. "Stochastic Approximations and Differential Inclusions." SIAM Journal on Control and Optimization 44, no. 1 (January 2005): 328–48. http://dx.doi.org/10.1137/s0363012904439301.

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2

Ekhaguere, G. O. S. "Lipschitzian quantum stochastic differential inclusions." International Journal of Theoretical Physics 31, no. 11 (November 1992): 2003–27. http://dx.doi.org/10.1007/bf00671969.

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3

Perkins, Steven, and David S. Leslie. "Asynchronous Stochastic Approximation with Differential Inclusions." Stochastic Systems 2, no. 2 (December 2012): 409–46. http://dx.doi.org/10.1287/11-ssy056.

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4

Michta, Mariusz. "Optimal solutions to stochastic differential inclusions." Applicationes Mathematicae 29, no. 4 (2002): 387–98. http://dx.doi.org/10.4064/am29-4-2.

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5

Kisielewicz, Michał. "Stochastic differential inclusions and diffusion processes." Journal of Mathematical Analysis and Applications 334, no. 2 (October 2007): 1039–54. http://dx.doi.org/10.1016/j.jmaa.2007.01.027.

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6

Kisielewicz, Michał. "Stochastic representation of partial differential inclusions." Journal of Mathematical Analysis and Applications 353, no. 2 (May 2009): 592–606. http://dx.doi.org/10.1016/j.jmaa.2008.12.022.

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7

Michta, Mariusz, and Kamil Łukasz Świa̧tek. "Stochastic inclusions and set-valued stochastic equations driven by a two-parameter Wiener process." Stochastics and Dynamics 18, no. 06 (October 29, 2018): 1850047. http://dx.doi.org/10.1142/s0219493718500478.

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In the paper we study properties of solutions to stochastic differential inclusions and set-valued stochastic differential equations driven by a two-parameter Wiener process. We establish new connections between their solutions. We prove that attainable sets of solutions to such inclusions are subsets of values of multivalued solutions of associated set-valued stochastic equations. Next we show that every solution to stochastic inclusion is a continuous selection of a multivalued solution of an associated set-valued stochastic equation. Additionally we establish other properties of such solutions. The results obtained in the paper extends results dealing with this topic known both in deterministic and stochastic cases.

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8

Malinowski, Marek T., and Mariusz Michta. "The interrelation between stochastic differential inclusions and set-valued stochastic differential equations." Journal of Mathematical Analysis and Applications 408, no. 2 (December 2013): 733–43. http://dx.doi.org/10.1016/j.jmaa.2013.06.055.

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9

Papageorgiou, Nikolaos S. "Random fixed points and random differential inclusions." International Journal of Mathematics and Mathematical Sciences 11, no. 3 (1988): 551–59. http://dx.doi.org/10.1155/s0161171288000663.

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In this paper, first, we study random best approximations to random sets, using fixed point techniques, obtaining this way stochastic analogues of earlier deterministic results by Browder-Petryshyn, KyFan and Reich. Then we prove two fixed point theorems for random multifunctions with stochastic domain that satisfy certain tangential conditions. Finally we consider a random differential inclusion with upper semicontinuous orientor field and establish the existence of random solutions.

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10

Chaouche, Meryem, and Toufik Guendouzi. "Stochastic differential inclusions with Hilfer fractional derivative." Annals of the University of Craiova, Mathematics and Computer Science Series 49, no. 1 (June 24, 2022): 158–73. http://dx.doi.org/10.52846/ami.v49i1.1524.

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In this paper, we study the existence of mild solutions of Hilfer fractional stochastic differential inclusions driven by sub fractional Brownian motion in the cases when the multivalued map is convex and non convex. The results are obtained by using fixed point theorem. Finally an example is given to illustrate the obtained results.

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11

Gliklikh, Yu E., and A. V. Makarova. "On Stochastic Differential Inclusions with Current Velocities." Journal of Computational and Engineering Mathematics 2, no. 3 (2015): 25–33. http://dx.doi.org/10.14529/jcem150303.

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12

Ahmed, N. U. "Nonlinear stochastic differential inclusions on balance space." Stochastic Analysis and Applications 12, no. 1 (January 1994): 1–10. http://dx.doi.org/10.1080/07362999408809334.

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13

Makarova, A. "Оn stochastic differential inclusions with current velocites." Актуальные направления научных исследований XXI века: теория и практика 2, no. 4 (October 3, 2014): 108–11. http://dx.doi.org/10.12737/5126.

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14

Kravets, T. N. "On the problem of stochastic differential inclusions." Journal of Soviet Mathematics 53, no. 4 (February 1991): 398–403. http://dx.doi.org/10.1007/bf01098488.

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15

Ahmed, Hamdy M., Mahmoud M. El-Borai, Wagdy El-Sayed, and Alaa Elbadrawi. "Null Controllability of Hilfer Fractional Stochastic Differential Inclusions." Fractal and Fractional 6, no. 12 (December 5, 2022): 721. http://dx.doi.org/10.3390/fractalfract6120721.

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This paper gives the null controllability for nonlocal stochastic differential inclusion with the Hilfer fractional derivative and Clarke subdifferential. Sufficient conditions for null controllability of nonlocal Hilfer fractional stochastic differential inclusion are established by using the fixed-point approach with the proof that the corresponding linear system is controllable. Finally, the theoretical results are verified with an example.

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16

Mshary, Noorah, Hamdy M. Ahmed, Ahmed S. Ghanem, and A. M. Sayed Ahmed. "Hilfer-Katugampola fractional stochastic differential inclusions with Clarke sub-differential." Heliyon 10, no. 8 (April 2024): e29667. http://dx.doi.org/10.1016/j.heliyon.2024.e29667.

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17

Balasubramaniam, P. "Existence of solutions of functional stochastic differential inclusions." Tamkang Journal of Mathematics 33, no. 1 (March 31, 2002): 25–34. http://dx.doi.org/10.5556/j.tkjm.33.2002.302.

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18

Meghnafi, Mustapha, Mohamed Ali Hammami, and Tayeb Blouhi. "Existence results on impulsive stochastic semilinear differential inclusions." International Journal of Dynamical Systems and Differential Equations 11, no. 2 (2021): 131. http://dx.doi.org/10.1504/ijdsde.2021.115179.

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19

Meghnafi, Mustapha, Mohamed Ali Hammami, and Tayeb Blouhi. "Existence results on impulsive stochastic semilinear differential inclusions." International Journal of Dynamical Systems and Differential Equations 11, no. 2 (2021): 131. http://dx.doi.org/10.1504/ijdsde.2021.10037985.

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20

Yun, Yong-Sik. "THE BOUNDEDNESS OF SOLUTIONS FOR STOCHASTIC DIFFERENTIAL INCLUSIONS." Bulletin of the Korean Mathematical Society 40, no. 1 (February 1, 2003): 159–65. http://dx.doi.org/10.4134/bkms.2003.40.1.159.

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21

Li, Yong, and Bing Liu. "Boundary controllability of non-linear stochastic differential inclusions." Applicable Analysis 87, no. 6 (June 2008): 709–22. http://dx.doi.org/10.1080/00036810802213231.

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22

Ton, Bui An. "Optimal control for n-person differential stochastic inclusions." Stochastic Analysis and Applications 17, no. 6 (January 1999): 911–35. http://dx.doi.org/10.1080/07362999908809643.

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23

Ekhaguere, G. O. S. "Quantum stochastic differential inclusions of hypermaximal monotone type." International Journal of Theoretical Physics 34, no. 3 (March 1995): 323–53. http://dx.doi.org/10.1007/bf00671595.

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24

Benaïm, Michel, Josef Hofbauer, and Sylvain Sorin. "Stochastic Approximations and Differential Inclusions, Part II: Applications." Mathematics of Operations Research 31, no. 4 (November 2006): 673–95. http://dx.doi.org/10.1287/moor.1060.0213.

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25

Ayoola, E. O. "Error Estimates for Discretized Quantum Stochastic Differential Inclusions." Stochastic Analysis and Applications 21, no. 6 (January 11, 2003): 1215–30. http://dx.doi.org/10.1081/sap-120026104.

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26

Michta, Mariusz. "On connections between stochastic differential inclusions and set-valued stochastic differential equations driven by semimartingales." Journal of Differential Equations 262, no. 3 (February 2017): 2106–34. http://dx.doi.org/10.1016/j.jde.2016.10.039.

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27

Gliklikh, Yuri E., and Andrei V. Obukhovski. "Stochastic differential inclusions of Langevin type on Riemannian manifolds." Discussiones Mathematicae. Differential Inclusions, Control and Optimization 21, no. 2 (2001): 173. http://dx.doi.org/10.7151/dmdico.1023.

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28

Michta, Mariusz. "Weak solutions of stochastic differential Inclusions and their compactness." Discussiones Mathematicae. Differential Inclusions, Control and Optimization 29, no. 1 (2009): 91. http://dx.doi.org/10.7151/dmdico.1106.

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29

Roth, Grégory, and William H. Sandholm. "Stochastic Approximations with Constant Step Size and Differential Inclusions." SIAM Journal on Control and Optimization 51, no. 1 (January 2013): 525–55. http://dx.doi.org/10.1137/110844192.

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30

Gliklikh, Yuri E., and Alla V. Makarova. "On solvability of stochastic differential inclusions with current velocities." Applicable Analysis 91, no. 9 (September 2012): 1731–39. http://dx.doi.org/10.1080/00036811.2011.579565.

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31

Kravets, T. N. "On the stability of solutions of stochastic differential inclusions." Ukrainian Mathematical Journal 47, no. 4 (April 1995): 640–44. http://dx.doi.org/10.1007/bf01056052.

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32

Kravets, T. N. "On the approximation of solutions of stochastic differential inclusions." Journal of Soviet Mathematics 53, no. 1 (January 1991): 44–48. http://dx.doi.org/10.1007/bf01104049.

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33

Antonelli, Peter L., and Vlastimil Křivan. "Fuzzy differential inclusions as substitutes for stochastic differential equations in population biology." Open Systems & Information Dynamics 1, no. 2 (June 1992): 217–32. http://dx.doi.org/10.1007/bf02228945.

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34

Shukla, Anurag, Sumati Kumari Panda, Velusamy Vijayakumar, Kamalendra Kumar, and Kothandabani Thilagavathi. "Approximate Controllability of Hilfer Fractional Stochastic Evolution Inclusions of Order 1 < q < 2." Fractal and Fractional 8, no. 9 (August 24, 2024): 499. http://dx.doi.org/10.3390/fractalfract8090499.

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This paper addresses the approximate controllability results for Hilfer fractional stochastic differential inclusions of order 1<q<2. Stochastic analysis, cosine families, fixed point theory, and fractional calculus provide the foundation of the main results. First, we explored the prospects of finding mild solutions for the Hilfer fractional stochastic differential equation. Subsequently, we determined that the specified system is approximately controllable. Finally, an example displays the theoretical application of the results.

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35

Li, Yong, and Qiang Zou. "Controllability of Nonlinear Neutral Stochastic Differential Inclusions with Infinite Delay." Mathematical Problems in Engineering 2013 (2013): 1–13. http://dx.doi.org/10.1155/2013/419156.

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The paper is concerned with the controllability of nonlinear neutral stochastic differential inclusions with infinite delay in a Hilbert space. Sufficient conditions for the controllability are obtained by using a fixed-point theorem for condensing maps due to O'Regan.

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36

Blouhi, Tayeb, Mohamed Ferhat, and Safia Benmansour. "Existence for stochastic sweeping process with fractional Brownian motion." Studia Universitatis Babes-Bolyai Matematica 67, no. 4 (December 1, 2022): 749–71. http://dx.doi.org/10.24193/subbmath.2022.4.07.

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"This paper is devoted to the study of a convex stochastic sweeping process with fractional Brownian by time delay. The approach is based on dis- cretizing stochastic functional differential inclusions."

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37

Sivasankar, Sivajiganesan, and Ramalingam Udhayakumar. "Hilfer Fractional Neutral Stochastic Volterra Integro-Differential Inclusions via Almost Sectorial Operators." Mathematics 10, no. 12 (June 15, 2022): 2074. http://dx.doi.org/10.3390/math10122074.

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In our paper, we mainly concentrate on the existence of Hilfer fractional neutral stochastic Volterra integro-differential inclusions with almost sectorial operators. The facts related to fractional calculus, stochastic analysis theory, and the fixed point theorem for multivalued maps are used to prove the result. In addition, an illustration of the principle is provided.

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38

Vinodkumar, A., and A. Boucherif. "Existence Results for Stochastic Semilinear Differential Inclusions with Nonlocal Conditions." International Journal of Stochastic Analysis 2011 (November 30, 2011): 1–17. http://dx.doi.org/10.1155/2011/784638.

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We discuss existence results of mild solutions for stochastic differential inclusions subject to nonlocal conditions. We provide sufficient conditions in order to obtain a priori bounds on possible solutions of a one-parameter family of problems related to the original one. We, then, rely on fixed point theorems for multivalued operators to prove our main results.

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39

Raczynski, Stanislaw. "A market model: uncertainty and reachable sets." International Journal for Simulation and Multidisciplinary Design Optimization 6 (2015): A2. http://dx.doi.org/10.1051/smdo/2015002.

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Uncertain parameters are always present in models that include human factor. In marketing the uncertain consumer behavior makes it difficult to predict the future events and elaborate good marketing strategies. Sometimes uncertainty is being modeled using stochastic variables. Our approach is quite different. The dynamic market with uncertain parameters is treated using differential inclusions, which permits to determine the corresponding reachable sets. This is not a statistical analysis. We are looking for solutions to the differential inclusions. The purpose of the research is to find the way to obtain and visualise the reachable sets, in order to know the limits for the important marketing variables. The modeling method consists in defining the differential inclusion and find its solution, using the differential inclusion solver developed by the author. As the result we obtain images of the reachable sets where the main control parameter is the share of investment, being a part of the revenue. As an additional result we also can define the optimal investment strategy. The conclusion is that the differential inclusion solver can be a useful tool in market model analysis.

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40

Sakthivel, R., Yong Ren, Amar Debbouche, and N. I. Mahmudov. "Approximate controllability of fractional stochastic differential inclusions with nonlocal conditions." Applicable Analysis 95, no. 11 (September 28, 2015): 2361–82. http://dx.doi.org/10.1080/00036811.2015.1090562.

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41

Kisielewicz, Michał. "Weak compactness of weak solutions sets to stochastic differential inclusions." Stochastic Analysis and Applications 38, no. 3 (January 16, 2020): 506–26. http://dx.doi.org/10.1080/07362994.2019.1702884.

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42

Huang, Jun, Zhengzhi Han, Xiushan Cai, and Leipo Liu. "Control of time-delayed linear differential inclusions with stochastic disturbance." Journal of the Franklin Institute 347, no. 10 (December 2010): 1895–906. http://dx.doi.org/10.1016/j.jfranklin.2010.10.008.

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43

Atar, Rami, Amarjit Budhiraja, and Kavita Ramanan. "Deterministic and stochastic differential inclusions with multiple surfaces of discontinuity." Probability Theory and Related Fields 142, no. 1-2 (January 31, 2008): 249–83. http://dx.doi.org/10.1007/s00440-007-0104-z.

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44

Toufik, Guendouzi. "Existence and Controllability Results for Fractional Stochastic Semilinear Differential Inclusions." Differential Equations and Dynamical Systems 23, no. 3 (August 27, 2014): 225–40. http://dx.doi.org/10.1007/s12591-014-0217-7.

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45

Michta, Mariusz. "On Weak Solutions to Stochastic Differential Inclusions Driven by Semimartingales." Stochastic Analysis and Applications 22, no. 5 (January 2004): 1341–61. http://dx.doi.org/10.1081/sap-200026471.

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46

Kumar, Surendra, and Shobha Yadav. "Approximate controllability for a new class of stochastic functional differential inclusions with infinite delay." Random Operators and Stochastic Equations 30, no. 3 (September 1, 2022): 221–39. http://dx.doi.org/10.1515/rose-2022-2088.

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Abstract This manuscript investigates the approximate controllability for a wide range of infinite-delayed semilinear stochastic differential inclusions. First, we construct the expression for a mild solution in terms of the fundamental solution. Then, employing the fixed point theorem for multivalued maps, we formulate a set of sufficient conditions to assure the existence of a solution for the aforementioned system. Further, the approximate controllability for the semilinear stochastic differential inclusion is investigated under the condition that the associated linear deterministic control system is approximately controllable. The discussed results are more general and a continuation of the ongoing research on this issue. Finally, an example is included to highlight the applicability of the considered results.

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47

Abuasbeh, Kinda, Azmat Ullah Khan Niazi, Hafiza Maria Arshad, Muath Awadalla, and Salma Trabelsi. "Approximate Controllability of Fractional Stochastic Evolution Inclusions with Non-Local Conditions." Fractal and Fractional 7, no. 6 (June 7, 2023): 462. http://dx.doi.org/10.3390/fractalfract7060462.

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This article investigates the approximate controllability of non-linear fractional stochastic differential inclusions with non-local conditions. We establish a set of sufficient conditions for their approximate controllability and provide results in terms of controllability for the fractional stochastic control system. Our approach relies on using fractional calculus and the fixed-point theorem for multiple-valued operators. Finally, we present an illustrative example to support our findings.

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48

Ayoola, E. O., and John O. Adeyeye. "Continuous Interpolation of Solution Sets of Lipschitzian Quantum Stochastic Differential Inclusions." Journal of Applied Mathematics and Stochastic Analysis 2007 (January 23, 2007): 1–12. http://dx.doi.org/10.1155/2007/80750.

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Given any finite set of trajectories of a Lipschitzian quantum stochastic differential inclusion (QSDI), there exists a continuous selection from the complex-valued multifunction associated with the solution set of the inclusion, interpolating the matrix elements of the given trajectories. Furthermore, the difference of any two of such solutions is bounded in the seminorm of the locally convex space of solutions.

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49

Papageorgiou, Nikolaos S. "On measurable multifunctions with stochastic domain." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 45, no. 2 (October 1988): 204–16. http://dx.doi.org/10.1017/s1446788700030111.

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AbstractIn this paper we prove several random fixed point theorems for multifunctions with a stochastic domain. Then those techniques are used to establish the existence of solutions for random differential inclusions. A useful tool in this process is a stochastic version of the Tietze extension theorems that we prove. Finally we present a stochastic version of the Riesz representation theorem for Hilbert spaces.

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50

Dikko, D. A. "Further results on the arcwise connectedness of solution sets of discontinuous quantum stochastic differential inclusions." Infinite Dimensional Analysis, Quantum Probability and Related Topics 23, no. 03 (September 2020): 2050022. http://dx.doi.org/10.1142/s0219025720500228.

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In the framework of the Hudson–Parthasarathy quantum stochastic calculus, we employ a recent generalization of the Michael selection results in the present noncommutative settings to prove that the function space of the matrix elements of solutions to discontinuous quantum stochastic differential inclusion (DQSDI) is arcwise connected.

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