High Order Stochastic Inclusions and Their Applications

REFERENCES

• Aase , K.K. , and S.A. Person . 1994 . Pricing of unit-linked live insurance policies . Scand. Actuarial J. 1 : 26 – 52 .
   Google Scholar
• Ahmed, N.U. 1994 . Nonlinear stochastic differential inclusions on Banach space . Stoch. Anal. Appl. 12 ( 1 ): 1 – 10 .
   Web of Science ®Google Scholar
• Ahmed , N.U. 1994. Optimal relaxed for nonlinear infinite dimensional stochastic differential inclusions. In Optimal Control of Differential Equations . Marcel Dekker : New York, 1–19.
   Google Scholar
• Ahmed , N.U. 2002 . Impulsive perturbation of C 0 semigroups and stochastic evolution inclusions . Disc. Math. DICO 22 ( 1 ): 125 – 149 .
   Google Scholar
• Aubin , J.P. , and A. Cellina . 1984 . Differential Inclusions . Noordhoff Leyden .
   Google Scholar
• Aubin , J.P. , and H. Frankowska . 1990 . Set-Valued Analysis . Boston : Birkhäuser .
   Google Scholar
• Aubin , J.P. , and G. Da Prato . 1995 . Stochastic Nagumo's viability theorem . Stoch. Anal. Appl. 13 ( 1 ): 1 – 11 .
   Web of Science ®Google Scholar
• Aubin , J.P. , and G. Da Prato . 1998 . The viability theorem for stochastic differential inclusions . Stoch. Anal. Appl . 16 : 1 – 15 .
   Web of Science ®Google Scholar
• Bachelier , L. 1900 . Théorie de la speculation . Annales de l’Ecole Normale Supérieure 17 : 21 – 86 .
   Google Scholar
• Bharucha-Reid , A.T. 1972 . Random Integral Equations: Mathematics in Science and Engineering 96 . New York : Academic Press .
   Google Scholar
• Billingsley , P. 1968 . Convergence of Probability Measures . New York : Wiley .
   Google Scholar
• Black , F. , and M. Scholes . 1973 . The prices of options and corporate liabilities . J. Political Economy 81 : 637 – 654 . [CROSSREF]
   Web of Science ®Google Scholar
• Bressan , A. , and G. Colombo . 1988 . Extensions and selections of maps with decomposable values . Studia Math. 90 : 69 – 86 .
   Web of Science ®Google Scholar
• Fryszkowski , A. 1983 . Continuous selections for a class of nonconvex multivalued maps . Studia Math. 76 : 163 – 174 .
   Web of Science ®Google Scholar
• Friedman , A. 1975 . Stochastic Differential Equations and Applications . NewYork : Academic Press .
   Google Scholar
• Gihman , I.I. , and A.V. Skorohod . 1975 . The Theory of Stochastic Processes III . Berlin : Springer .
   Google Scholar
• Hiai , F. , and H. Umegaki . 1977 . Integrals, conditional expectations, and martingales of multivalued functions . J. Multivar. Anal. 7 : 149 – 182 . [CROSSREF]
   Web of Science ®Google Scholar
• Jacod , J. , and J. Memin . 1981 . Weak and Strong Solutions of Stochastic Differential Equations: Existence and Stability . In Lect. Notes in Math. 851 . Berlin : Springer . 169 – 212 .
   Google Scholar
• Jacod , J. , and A.N. Shiryaev . 1987 . Limit Theorems for Stochastic Processes . New York : Springer .
   Google Scholar
• Karatzas , I. , and S. Shreve . 1988 . Brownian Motion and Stochastic Calculus . New York : Springer .
   Google Scholar
• Kisielewicz , M. 1991 . Differential Inclusions and Optimal Control . Warszawa-Dordrecht : Kluwer Acad. Publ. and Polish Sci. Publ. .
   Google Scholar
• Kisielewicz , M. 1997 . Set-valued stochastic integrals and stochastic inclusions . Stoch. Anal. Appl . 15 ( 5 ): 783 – 800 .
   Web of Science ®Google Scholar
• Kisielewicz , M. 2001 . Weak compacteness of solution sets to stochastic differential inclusions with convex right-hand side . Topol. Meth. Nonlin. Anal. 18 : 149 – 169 .
   Google Scholar
• Kisielewicz , M. , M. Michta , and J. Motyl . 2003 . Set–valued approach to stochastic control part I and part II . Dynamic Syst. Appl. 12 : 405 – 432 and 433–466 .
   Web of Science ®Google Scholar
• Levakov , A.A. 1997 . Stochastic differential inclusions . J. Differ. Eq. 2 ( 33 ): 212 – 221 .
   Google Scholar
• Liptser , R.S. , and A.N. Shiryaev . 1978. Statistics of Random Processes . New York : Springer.
   Google Scholar
• Mao , X. 1997 . Stochastic Differential Equations and Their Applications . Chichester : Horwood Publishing .
   Google Scholar
• Marcus , L. , and A. Weerasinghe . 1988 . Stochastic oscillators . J. Differ. Eq. 71 ( 2 ): 288 – 314 . [CROSSREF]
   Web of Science ®Google Scholar
• Michta , M. 2002 . Stochastic inclusions with multivalued integrators . Stoch. Anal. Appl. 20 ( 4 ): 847 – 862 . [CROSSREF]
   Web of Science ®Google Scholar
• Michta , M. 2002 . Optimal solutions to stochastic differential inclusions . Applicationes Math. 29 : 387 – 398 .
   Google Scholar
• Motyl , J. 1998 . Stochastic functional inclusion driven by semimartingale . Stoch. Anal. Appl. 16 ( 3 ): 517 – 532 .
   Web of Science ®Google Scholar
• Motyl , J. 1998 . Existence of solutions of set-valued Ito equation . Bull. Acad. Pol. Sci. 46 : 419 – 430 .
   Google Scholar
• Motyl , J. 2001 . Monotone operators in stochastic set-valued equations . Nonlinear Analysis 47 : 49 – 55 . [CROSSREF]
   Web of Science ®Google Scholar
• Protter , P. 1990 . Stochastic Integration and Differential Equations: A New Approach . New York : Springer .
   Google Scholar
• Shiryaev , A.N. 1999 . Essentials of Stochastic Finance, Facts, Models, Theory, Advanced Series on Statistical Science and Applied Probability . Vol. 3 . World Science Publisher : Singapore, New Jersey London, Hongkong .
   Google Scholar
• Tsokos , C.P. , and W.J. Padgett . 1974 . Random Integral Equations with Applications to Life Sciences and Engineering, Mathematics in Science and Engineering 108 . New York : Academic Press .
   Google Scholar
• Stroock , D. , and S.R. Varadhan . 1975 . Multidimensional Diffusion Processes . New York : Springer .
   Google Scholar