Abstract
In this chapter, we study Yosida approximations of various classes of stochastic differential equations, including such equations with delays and controlled stochastic differential equations.
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References
N. U. Ahmed Semigroup Theory with Applications to Systems and Control, Pitman Research Notes in Mathematics Series, Vol. 246, Longman Scientific and Technical Copublished with John Wiley and Sons, Inc., New York, 1991.
N. U. Ahmed Measure solutions for evolution equations with discontinuous vector fields, Nonlinear Functional Anal. Appl. 9, 467–484, 2004.
N. U. Ahmed and X. Ding A semilinear McKean-Vlasov stochastic evolution equation in Hilbert spaces, Stochastic Proc. Appl. 60, 65–85, 1995.
H. Becker and V. Mandrekar On the existence of optimal random controls, J. Math. Mechan. 18, 1151–1166, 1969.
F. Biagini, Y. Hu, B. Oksendal and T. Zhang Stochastic Calculus for Fractional Brownian Motion and Applications, Springer, 2008.
T. Caraballo, M. J. Garrido-Atienza and T. Taniguchi The existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional Brownian motion, Nonlinear Anal. 74, 3671–3684, 2011.
G. Chen and R. Grimmer Semigroups and integral equations, J. Integral Eqns. 2, 133–154, 1980.
R. F. Curtain and A. J. Pritchard Infinite Dimensional Linear System Theory, Lecture Notes in Control and Information Sciences No. 8, Springer-Verlag, NY, Berlin, 1978.
G. Da Prato and J. Zabczyk Stochastic Equations in Infinite Dimensions, Cambridge Univ. Press, 1992.
N. Dunford and J. T. Schwartz Linear Operators, Part 1, Interscience Publishers, NY, 1958.
S. Hu and N. S. Papageorgiou Handbook of Multivalued Analysis, Vol 1, Theory, Kluwer Academic Publ., Dordrecht/ Boston/London, 1997.
A. Ichikawa Dynamic programming approach to stochastic evolution equations, SIAM Journal on Control and Optimization, 17, 152–174, 1979.
A. Ichikawa Optimal control of a linear stochastic evolution equation with state and control dependent noise, Proc. IMA Conference, Recent Theoretical Developments in Control, Leicester, England, Academic Press, 1976.
D. Kannan and A. T. Bharucha-Reid On a stochastic integrodifferential evolution equation of Volterra type, J. Integral eqns. 10, 351–379, 1985.
W. Liu and M. Röckner SPDE in Hilbert space with locally monotone coefficients, J. Functional Anal. 259, No. 11, 2902–2922, 2010.
E. Pardoux Stochastic partial differential equations and filtering of diffusion processes, Stochastics 3, 127–167, 1979.
A. Pazy Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, NY, USA, 1983.
C. Prévôt and M. Röckner A Concise Course on Stochastic Partial Differential Equations, Springer, 2007.
M. Stephan Yosida Approximations for Multivalued Stochastic Differential Equations on Banach Spaces via a Gelfand Triple, Doctoral Dissertation, Universit at Bielefeld, 2012.
E. Zeidler Nonlinear Functional Analysis and its Applications, IIA, Linear Monotone Operators, Springer-Verlag, NY, 1990.
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Govindan, T.E. (2016). Yosida Approximations of Stochastic Differential Equations. In: Yosida Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications. Probability Theory and Stochastic Modelling, vol 79. Springer, Cham. https://doi.org/10.1007/978-3-319-45684-3_3
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DOI: https://doi.org/10.1007/978-3-319-45684-3_3
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