Existence of solutions of set-valued Ito equation

• Autorzy: Motyl J.
• Języki publikacji: EN

Abstrakty

EN

In the paper, the problem of existence of solution to the stochastic functional inclusion x [...] is investigated under some assumption of the dissipativity type on set-valued functions A and B.

Słowa kluczowe

EN

control; dissipative set-valued function; Ito formula; measurable selector; predicable process; probabilility theory; stochastic analysis; stochastic integral; stochastic processes; Yosida approximation

PL

aproksymacja Yosidy; całka stochastyczna; mierzalny selektor; procesy predykacyjne; systems theory \\@en\; teoria sterowania; teoria systemów; wzór Ito

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 1998
• Tom: Vol. 46, no. 4
• Strony: 419--430
• Opis fizyczny: Bibliogr. 36 poz.,

Twórcy

autor

Motyl J.

• Institute of Mathematics, Zielona Góra Technical University, Podgórna 50, 65-246 Zielona Góra, Poland

Bibliografia

• [1] N. U. Ahmed, Semigroup theory with applications to systems and control, J. Wiley and Sons Ltd., London 1991.
• [2] I. I. Gihman, A. V. Skorohod, Controlled Stochastic Processes; Springer- Verlag, New York 1979.
• [3] N. V. Krylov, Controlled Diffusion Processes, Appl. Math., Springer-Verlag, New York 1980.
• [4] R. W. Rishel, W. H. Fleming, Deterministic and Stochastic Optimal Control, Appl. Math., Springer-Verlag, New York 1975.
• [5] J. P. Aubin, A. Cellina, Differential Inclusions, Noordhoff Leyden 1984.
• [6] M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer Acad. Publ. and Polish Sci. Publ., Warszawa-Dordrecht 1991.
• [7] A. G. Dа Рrato, H. Frankowskа, A stochastic Filippov theorem, Stoch. Аnаl. Аррl., 12(4) (1994) 409-426.
• [8] F. Hiai, Multivalued stochastic iniegrals and stochastic differential inclusions, Division of Applied Mathematics, Research Instituto of Applied Electricity, Sapporo 060, Japan, unpublished manuscript.
• [9] M. Kisielewicz, Properties of solution set of stochastic inclusions, J. Appl. Mado. Stoch. Anal., 6 (1993) 217--236.
• [10] J. Motyl, Stochastic functional inclusion driven by semimartingale, Stoch. Anal. Appl., 16(3) (1998), 517-532.
• [11] А. G. Da Prato, .T. Zabczуk, Stochastic equations in infinite dimensions, Cambridge University Press 1992.
• [12] P. Kotelenez, A stopped Doob inequality for stochastic convolution integrals and stochastic evolution equations, Stoch. Anal. Appl., 2 (1984) 245-265.
• [13] E. Cépa, Equations différentielles stochsastiques multivoques, Seminaire de Probabilites 29, Lect. Notes Math., 1613 (1995) 86-107.
• [14] Т. N. Kravec, To the question on stochastic differential inclusions (in Russian), Theory of Random Processes, 15 (1987) 54-59.
• [15] P. Kree, Diffusion Equation for Multivalued Stochastic Differential Equations, J. Funct. Anal., 49 (1982) 73-90.
• [16] R. Pettersson, Yosida approximations for mulvalued stochast,żc differential equations, Stochastics and Stoch. Reports, 52 (1995) 107-120.
• [17] R.. Pettersson, Existence theorem zioriro and Wong Zakai approximations for multivalued stochastic differential equations. Probab. Math. Statist., 17(1) (1997) 29-45.
• [18] E. Pardoux. Éequations аux derivées partielles stochastiques nonlinéaries monotones, Thése, Universitę Paris XI 1975.
• [19] A. G. Da Prato, M. Ianelli, L. Tubarо, Dassipative functions and finite dimensional stochastic differential equations, J. Mаth. Puris et Appl., 57 (1978).
• [20] A. G. Da Prato, C. Tudor, Periodice and almost periodic solutions for semilinear stochastic equations, Stoch. Anal. Appl., 13(1) (1995) 13-33.
• [21] F. Flandoli, A stochastic reaction-diffusion equation with, multiplicative noise, Appl. Math. Letters, 4 (1991) 45-48.
• [22] J. Gуöngy, N. V. Krylov, On stochastic equations with respect, to semi- mаrtingales, Stochastics, 4 (1980) 1-21.
• [23] J. Gуöngy y, N.V. Krylov, Existence of strong solutions for Itô stochastis equations via approximations. Probab. Theory Balat. Fields, 105 (1996) 143-158.
• [24] J. Jacod, Une condition d'Exitenc et d'uicité pour les solutions fortes d'equations différentielless stochastiques, Stochastics, 4 (1980) 23-38.
• [25] N. V. Krylov, A simple proof of thee existence of a solution of Itô's eguation with, monotone coefficients, Тheоrу Probab. Appl., 3,(1991) 583-587.
• [26] N. V. Krylov, B. L. Rozovskii, On stochastic evolution equations (in Russian). Modern Ргоblems in Math. VINITI, 14 (1979) 71-146.
• [27] L. Тubагo, On abstract, stochastic differential equation in Hilbert spaces mich dissipative drift, Stoch. Anal. Appl.. 1(2) (1983) 205 21.1.
• [28] N. U. Ahmed Ј. Existence of solutions of nonlinear stochastic differential inclusions on Banach spaces, Proc. World Congress Nonlinear Analysis, еd.: Walter de Gruyter 1993.
• [29] N. U. Ahmed; Optimal relaxed controls for nonlinear infinite dimensional stochastic differential inclusions, Optimal Control of Differential Equations, M. Dekker, Lecture Notes, 160 (1994) 1-19.
• [30] J. Мotyl, On the solution of stochastic differential inclusion, J. Math. Anal. Appl., 192 (1995) 117-132.
• [31] V. Bаrbu, Nonlinear Semigroups aud Differential Equations in. Banach Spaces, Noordhoff Leyden 1976.
• [32] P. Protter, Stochastic Integration and Differential Equations: A New Арproach, Springer-Verlag, Niw York 1990.
• [33] R. Н. Martin Jr. .Nonlinear operators and differential equations in Banach spaces, J. Wiley and Sons Ltd., New York 1976.
• [34] F. E. Browder, The solvability of nonlinear functional equations, Duke Math. J., 29 (1963) 557-566.
• [35] C. P. Tsokos, W. J. Pаdgett; Random Integral Equations with Applicaions to Life Sciences and, Engineering, Mathematics in Science and Engineering 108, Academic Press. New York 1974.
• [36] A. Т. Вhаruсhа-Rеid, Random Integral Equations, Math. Sci. Eng. 96, Academic Press, New York 1972.