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Volumn 21, Issue 2-3, 2012, Pages 293-318

On multivalued stochastic integral equations driven by a wiener process in the plane

Author keywords

Fuzzy stochastic integral equation; Random field; Set valued stochastic integral equation

Indexed keywords


EID: 84863499533     PISSN: 10562176     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (7)

References (53)
  • 1
    • 84948305154 scopus 로고
    • Nonlinear stochastic differential inclusions on Banach spaces
    • N. U. Ahmed, Nonlinear stochastic differential inclusions on Banach spaces, Stock. Anal. Appl., 12:1-10, 1994.
    • (1994) Stock. Anal. Appl. , vol.12 , pp. 1-10
    • Ahmed, N.U.1
  • 2
    • 1542326693 scopus 로고    scopus 로고
    • Impulsive perturbation of Co semigroups and stochastic evolution inclusions
    • N. U. Ahmed, Impulsive perturbation of Co semigroups and stochastic evolution inclusions, Discuss. Math. Differ. Incl. Control Optim., 22:125-149, 2002.
    • (2002) Discuss. Math. Differ. Incl. Control Optim. , vol.22 , pp. 125-149
    • Ahmed, N.U.1
  • 3
    • 0037652915 scopus 로고
    • Optimal relaxed controls for nonlinear infinite dimensional stochastic differential inclusions, Optimal Control of Differential Equations
    • N. U. Ahmed, Optimal relaxed controls for nonlinear infinite dimensional stochastic differential inclusions, Optimal Control of Differential Equations, M. Dekker Lect. Notes, 160:1-19, 1994.
    • (1994) M. Dekker Lect. Notes , vol.160 , pp. 1-19
    • Ahmed, N.U.1
  • 4
    • 34248570683 scopus 로고    scopus 로고
    • Differential inclusions operator valued measures and optimal control
    • N. U. Ahmed, Differential inclusions operator valued measures and optimal control, Dynam. Systems Appl., 16:13-36, 2007.
    • (2007) Dynam. Systems Appl. , vol.16 , pp. 13-36
    • Ahmed, N.U.1
  • 5
    • 0012777172 scopus 로고
    • A calculus for set-valued maps and set-valued evolusion equations
    • Z. Artstein, A calculus for set-valued maps and set-valued evolusion equations, Set- Valued Anal., 3:216-261, 1995.
    • (1995) Set- Valued Anal. , vol.3 , pp. 216-261
    • Artstein, Z.1
  • 6
    • 0009095592 scopus 로고
    • Stochastic integrals in the plane
    • R. Cairoli and J. B. Walsh, Stochastic integrals in the plane. Acta Math., 134:111-183, 1975.
    • (1975) Acta Math. , vol.134 , pp. 111-183
    • Cairoli, R.1    Walsh, J.B.2
  • 7
    • 12844285437 scopus 로고
    • Equazioni differenziali con soluzioni a valore compatto convesso
    • F. S. De Blasi and F. Iervolino, Equazioni differenziali con soluzioni a valore compatto convesso, Boll. Unione Math Ital., 4:194 501, 1969.
    • (1969) Boll. Unione Math Ital. , vol.4 , pp. 194501
    • De Blasi, F.S.1    Iervolino, F.2
  • 8
    • 34248587205 scopus 로고    scopus 로고
    • Banach-Saks-Mazur nad Kakutani-Ky-Fan theorems in spaces of multifunctions and applications to set differential inclusions, Dynam
    • F. S. De Blasi, Banach-Saks-Mazur nad Kakutani-Ky-Fan theorems in spaces of multifunctions and applications to set differential inclusions, Dynam. Systems Appl., 16:73 89, 2007.
    • (2007) Systems Appl. , vol.16 , pp. 7389
    • De Blasi, F.S.1
  • 12
    • 33746131887 scopus 로고
    • On the general theory of random fields on the plane
    • (in Russian)
    • A. A. Gushchin, On the general theory of random fields on the plane, (in Russian) Uspekhi Mat. Nauk, 37:53-74, 1982.
    • (1982) Uspekhi Mat. Nauk , vol.37 , pp. 53-74
    • Gushchin, A.A.1
  • 13
    • 14644437111 scopus 로고    scopus 로고
    • Set valued functions in Fréchet spaces: Continuity, Hukuhara differentiability and applications to set differential equations
    • DOI 10.1016/j.na.2005.01.004, PII S0362546X05000155
    • G. N. Galanis, T. Gnana Bhaskar, V. Lakshmikantham and P. K. Palamides, Set valued functions in Frechet spaces: continuity, Hukuhara differentiability and applications to set differential equations, Nonlinear Anal. TMA, 61:559-575, 2005. (Pubitemid 40319646)
    • (2005) Nonlinear Analysis, Theory, Methods and Applications , vol.61 , Issue.4 , pp. 559-575
    • Galanis, G.N.1    Bhaskar, T.G.2    Lakshmikantham, V.3    Palamides, P.K.4
  • 14
    • 0001577815 scopus 로고
    • Integrals, conditional expectations, and martingales of multivalued functions
    • F. Hiai and H. Umegaki, Integrals, conditional expectations, and martingales of multivalued functions, J. Multivariate Anal., 7:149 182, 1977.
    • (1977) J. Multivariate Anal. , vol.7 , pp. 149182
    • Hiai, F.1    Umegaki, H.2
  • 17
    • 84855346756 scopus 로고    scopus 로고
    • Some properties of set-valued stochastic integrals
    • M. Kisielewicz, Some properties of set-valued stochastic integrals, J. Math. Anal. Appl., 388:984 995,2012.
    • (2012) J. Math. Anal. Appl. , vol.388 , pp. 984995
    • Kisielewicz, M.1
  • 18
    • 12744250114 scopus 로고
    • Method of averaging for differential equations with compact convex valued solutions
    • M. Kisielewicz, Method of averaging for differential equations with compact convex valued solutions, Rend. Math., 6:397-408, 1976.
    • (1976) Rend. Math. , vol.6 , pp. 397-408
    • Kisielewicz, M.1
  • 19
    • 34248546421 scopus 로고    scopus 로고
    • Backward stochastic differential inclusions
    • M. Kisielewicz, Backward stochastic differential inclusions, Dynam. Systems Appl., 16:121-140, 2007.
    • (2007) Dynam. Systems Appl. , vol.16 , pp. 121-140
    • Kisielewicz, M.1
  • 20
    • 49249092574 scopus 로고    scopus 로고
    • Weak compactness of weak solutions to backward stochastic differential inclusions
    • M. Kisielewicz, Weak compactness of weak solutions to backward stochastic differential inclusions, Dynam. Systems Appl., 17:351-370, 2008.
    • (2008) Dynam. Systems Appl. , vol.17 , pp. 351-370
    • Kisielewicz, M.1
  • 21
    • 21144449034 scopus 로고    scopus 로고
    • Set-valued approach to stochastic control. Part I. Existence and regularity properties
    • M. Kisielewicz, M. Michta and J. Motyl, Set-valued approach to stochastic control. Part I. Existence and regularity properties, Dynam. Systems Appl., 12:405 431, 2003.
    • (2003) Dynam. Systems Appl. , vol.12 , pp. 405431
    • Kisielewicz, M.1    Michta, M.2    Motyl, J.3
  • 22
    • 21144449034 scopus 로고    scopus 로고
    • Set-valued approach to stochastic control. Part II. Viability and semimartingale issue
    • M. Kisielewicz, M. Michta and J. Motyl, Set-valued approach to stochastic control. Part II. Viability and semimartingale issue, Dynam. Systems Appl., 12:433 466, 2003.
    • (2003) Dynam. Systems Appl. , vol.12 , pp. 433466
    • Kisielewicz, M.1    Michta, M.2    Motyl, J.3
  • 23
    • 0038137267 scopus 로고    scopus 로고
    • Interconnection between set and fuzzy differential equations
    • V. Lakshmikantham, S. Lela and A. Vatsala, Interconnection between set and fuzzy differential equations, Nonlinear Anal. TMA, 54:351 360, 2003.
    • (2003) Nonlinear Anal. TMA , vol.54 , pp. 351360
    • Lakshmikantham, V.1    Lela, S.2    Vatsala, A.3
  • 25
    • 0041387380 scopus 로고    scopus 로고
    • Existence and interrelation between set and fuzzy differential equations
    • V. Lakshmikantham and A.A. Tolstonogov, Existence and interrelation between set and fuzzy differential equations, Nonlinear Anal. TMA, 55:255 268, 2003.
    • (2003) Nonlinear Anal. TMA , vol.55 , pp. 255268
    • Lakshmikantham, V.1    Tolstonogov, A.A.2
  • 27
    • 0030186933 scopus 로고    scopus 로고
    • Estimates on moments of the solutions to stochastic differential equations with respect to martingales in the plane
    • Z. Liang and M. Zheng, Estimates on moments of the solutions to stochastic differential equations with respect to martingales in the plane, Stochastic Process. Appl., 62:263 276, 1996.
    • (1996) Stochastic Process. Appl. , vol.62 , pp. 263276
    • Liang, Z.1    Zheng, M.2
  • 28
    • 69249232212 scopus 로고    scopus 로고
    • On random fuzzy differential equations
    • M. T. Malinowski, On random fuzzy differential equations, Fuzzy Sets and Systems, 160:3152-3165, 2009.
    • (2009) Fuzzy Sets and Systems , vol.160 , pp. 3152-3165
    • Malinowski, M.T.1
  • 29
    • 77953962287 scopus 로고    scopus 로고
    • Existence theorems for solutions to random fuzzy differential equations
    • M. T. Malinowski, Existence theorems for solutions to random fuzzy differential equations, Nonlinear Anal. TMA, 73:1515-1532, 2010.
    • (2010) Nonlinear Anal. TMA , vol.73 , pp. 1515-1532
    • Malinowski, M.T.1
  • 30
    • 84855205569 scopus 로고    scopus 로고
    • Strong solutions to stochastic fuzzy differential equations of Itô type
    • M. T. Malinowski, Strong solutions to stochastic fuzzy differential equations of Itô type, Math. Comput. Modelling, 55:918 928, 2012.
    • (2012) Math. Comput. Modelling , vol.55 , pp. 918928
    • Malinowski, M.T.1
  • 31
    • 80054884842 scopus 로고    scopus 로고
    • Random fuzzy differential equations under generalized Lipschitz condition
    • M. T. Malinowski, Random fuzzy differential equations under generalized Lipschitz condition, Nonlinear Anal. RWA, 13:860-881, 2012.
    • (2012) Nonlinear Anal. RWA , vol.13 , pp. 860-881
    • Malinowski, M.T.1
  • 32
    • 78650368831 scopus 로고    scopus 로고
    • Fuzzy stochastic integral equations. Dynam
    • M. T. Malinowski and M. Michta, Fuzzy stochastic integral equations. Dynam. Systems Appl., 19:473 493, 2010.
    • (2010) Systems Appl. , vol.19 , pp. 473493
    • Malinowski, M.T.1    Michta, M.2
  • 33
    • 79952031022 scopus 로고    scopus 로고
    • Stochastic fuzzy differential equations with an application
    • M. T. Malinowski and M. Michta, Stochastic fuzzy differential equations with an application, Kybernetika, 41:123 143, 2011.
    • (2011) Kybernetika , vol.41 , pp. 123143
    • Malinowski, M.T.1    Michta, M.2
  • 34
    • 2442558298 scopus 로고    scopus 로고
    • Optimal solutions to stochastic differential inclusions
    • M. Michta, Optimal solutions to stochastic differential inclusions, Applicationes Math., 29:387-398, 2002. (Pubitemid 36218954)
    • (2002) Applicationes Math. , vol.29 , Issue.4 , pp. 387-398
    • Michta, M.1
  • 35
    • 5644257295 scopus 로고    scopus 로고
    • On weak solutions to stochastic differential inclusions driven by semimartingales
    • DOI 10.1081/SAP-200026471
    • M. Michta, On weak solutions to stochastic differential inclusions driven by semimartingales, Stoch. Anal. Appl., 22:1341-1361, 2004. (Pubitemid 39374461)
    • (2004) Stochastic Analysis and Applications , vol.22 , Issue.5 , pp. 1341-1361
    • Michta, M.1
  • 36
    • 79958122301 scopus 로고    scopus 로고
    • On set-valued stochastic integrals and fuzzy stochastic equations
    • M. Michta, On set-valued stochastic integrals and fuzzy stochastic equations, Fuzzy Sets and Systems, 177:1 19, 2011.
    • (2011) Fuzzy Sets and Systems , vol.177 , pp. 119
    • Michta, M.1
  • 37
    • 23944438953 scopus 로고    scopus 로고
    • Weak solutions to a stochastic inclusion with multivalued integrators
    • M. Michta and J. Motyl, Weak solutions to a stochastic inclusion with multivalued integrator, Dynam. Systems Appl., 14:323-334, 2005. (Pubitemid 41183710)
    • (2005) Dynamic Systems and Applications , vol.14 , Issue.2 , pp. 323-334
    • Michta, M.1    Dhage, B.C.2    Motyl, J.3
  • 38
    • 33646340695 scopus 로고    scopus 로고
    • Second order stochastic inclusions and equations
    • M. Michta and J. Motyl, Second order stochastic inclusions and equations, Dynam. Systems Appl, 15:301-315, 2006.
    • (2006) Dynam. Systems Appl , vol.15 , pp. 301-315
    • Michta, M.1    Motyl, J.2
  • 39
    • 34248547653 scopus 로고    scopus 로고
    • Set valued Stratonovich integral and Stratonovich type stochastic inclusion
    • M. Michta and J. Motyl, Set valued Stratonovich integral and Stratonovich type stochastic inclusion, Dynam. Systems Appl., 16:141-154, 2007.
    • (2007) Dynam. Systems Appl. , vol.16 , pp. 141-154
    • Michta, M.1    Motyl, J.2
  • 40
    • 79958130642 scopus 로고    scopus 로고
    • Set-valued stochastic differential equations in M-type 2 Banach space
    • I. Mitoma, Y. Okazaki and J. Zhang, Set-valued stochastic differential equations in M-type 2 Banach space, Comm. Stock. Anal., 4:215 -237, 2010.
    • (2010) Comm. Stock. Anal. , vol.4 , pp. 215-237
    • Mitoma, I.1    Okazaki, Y.2    Zhang, J.3
  • 42
    • 58149131672 scopus 로고    scopus 로고
    • On stochastic differential equations with fuzzy set coefficients
    • Springer, Berlin
    • Y. Ogura, On stochastic differential equations with fuzzy set coefficients. In: Soft Methods for Handling Variability and Imprecision, pp. 263 270, Springer, Berlin, 2008.
    • (2008) Soft Methods for Handling Variability and Imprecision , pp. 263270
    • Ogura, Y.1
  • 44
    • 46749092862 scopus 로고    scopus 로고
    • Supremum metric on the space of fuzzy sets and common fixed point theorems for fuzzy mappings
    • D. Qiu and L. Shu, Supremum metric on the space of fuzzy sets and common fixed point theorems for fuzzy mappings, Inform. Sci., 178:3595 3604, 2008.
    • (2008) Inform. Sci. , vol.178 , pp. 35953604
    • Qiu, D.1    Shu, L.2
  • 45
    • 34250097130 scopus 로고
    • A stochastic integral for Gaussian processes in the plane
    • E.N. Strukov, A stochastic integral for Gaussian processes in the plane, J. Math. Sci., 3:2486 2491, 1988.
    • (1988) J. Math. Sci. , vol.3 , pp. 24862491
    • Strukov, E.N.1
  • 47
    • 74549189771 scopus 로고
    • Stochastic integrals equations in the plane
    • C. Tudor, Stochastic integrals equations in the plane, Rev. Roumaine Math. Pures Appl., 26:507-538, 1981.
    • (1981) Rev. Roumaine Math. Pures Appl. , vol.26 , pp. 507-538
    • Tudor, C.1
  • 48
    • 84863432312 scopus 로고
    • Nonlinear stochastic functional intergal equations in the plane
    • J. Turo, Nonlinear stochastic functional intergal equations in the plane, J. Appl. Math. Stochastic Anal., 4:371-379, 1995.
    • (1995) J. Appl. Math. Stochastic Anal. , vol.4 , pp. 371-379
    • Turo, J.1
  • 49
    • 0000858834 scopus 로고
    • Martingales and stochastic integrals for processes with a multidimensional parameter
    • E. Wong and M. Zakai, Martingales and stochastic integrals for processes with a multidimensional parameter, Z. Wahrsch. Verw. Gebiete, 29:109 122, 1974.
    • (1974) Z. Wahrsch. Verw. Gebiete , vol.29 , pp. 109122
    • Wong, E.1    Zakai, M.2
  • 50
    • 84972514664 scopus 로고
    • Existence of strong solutions for stochastic differential equations in the plane
    • J. Yeh, Existence of strong solutions for stochastic differential equations in the plane. Pacific J. Math., 97:217-247, 1981.
    • (1981) Pacific J. Math. , vol.97 , pp. 217-247
    • Yeh, J.1
  • 51
    • 84967735788 scopus 로고
    • Existence of weak solutions to stochastic differential equations in the plane with continuous coefficients
    • J. Yeh, Existence of weak solutions to stochastic differential equations in the plane with continuous coefficients, Trans. Amer. Math. Soc., 290:345 361, 1985.
    • (1985) Trans. Amer. Math. Soc. , vol.290 , pp. 345361
    • Yeh, J.1
  • 52
    • 0008981560 scopus 로고
    • Uniqueness of strong solutions to stochastic differential equations in the plane with deterministic boundary process
    • J. Yeh, Uniqueness of strong solutions to stochastic differential equations in the plane with deterministic boundary process, Pacific J. Math., 128:391-400, 1987.
    • (1987) Pacific J. Math. , vol.128 , pp. 391-400
    • Yeh, J.1
  • 53
    • 33748486939 scopus 로고    scopus 로고
    • Non-Lipschitz stochastic differential equations driven by multi-parameter brownian motions
    • DOI 10.1142/S021949370600175X, PII S021949370600175X
    • X. Zhang and J. Zhu, Non-Lipschitz stochastic differential equations driven by multi-parameter Brownian motions, Stock. Dyn., 6:329-340, 2006. (Pubitemid 44355736)
    • (2006) Stochastics and Dynamics , vol.6 , Issue.3 , pp. 329-340
    • Zhang, X.1    Zhu, J.2


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