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Volumn 82, Issue 5, 2010, Pages 475-520

Jump-diffusions in Hilbert spaces: Existence, stability and numerics

Author keywords

High order numerical schemes; Mild and weak solutions; Stability results; Stochastic partial differential equations

Indexed keywords


EID: 77957869023     PISSN: 17442508     EISSN: 17442516     Source Type: Journal    
DOI: 10.1080/17442501003624407     Document Type: Article
Times cited : (69)

References (34)
  • 1
    • 60549097061 scopus 로고    scopus 로고
    • Existence of mild solutions for stochastic differential equations and semilinear equations with non Gaussian Lévy noise
    • S. Albeverio, V. Mandrekar, and B. Rudiger, Existence of mild solutions for stochastic differential equations and semilinear equations with non Gaussian Lévy noise, Stochastic Process. Appl. 119 (2008), pp. 835-863.
    • (2008) Stochastic Process. Appl , vol.119 , pp. 835-863
    • Albeverio, S.1    Mandrekar, V.2    Rudiger, B.3
  • 3
    • 78149321151 scopus 로고    scopus 로고
    • Martingale-valued measures, Ornstein-Uhlenbeck processes with jumps and operator self-decomposability in Hilbert space
    • D. Applebaum, Martingale-valued measures, Ornstein-Uhlenbeck processes with jumps and operator self-decomposability in Hilbert space, Seminaire de Probabilites 39 (2005), pp. 171-197.
    • (2005) Seminaire De Probabilites , vol.39 , pp. 171-197
    • Applebaum, D.1
  • 7
    • 0039740083 scopus 로고
    • A convergence result for stochastic partial differential equations
    • Z. Brzeźniak, M. Capiński, and F. Flandoli, A convergence result for stochastic partial differential equations, Stochastics 24(4) (1988), pp. 423-445.
    • (1988) Stochastics , vol.24 , Issue.4 , pp. 423-445
    • Brzeźniak, Z.1    Capińsk, M.2    Flandoli, F.3
  • 8
    • 43049114149 scopus 로고    scopus 로고
    • Itô'sformula in UMD Banach spaces and regularity of solutions of the Zakai equation
    • Z. Brzeźniak, J.M.A.M. van Neerven, M.C. Veraar, and L. Weis, Itô'sformula in UMD Banach spaces and regularity of solutions of the Zakai equation, J. Differential Equations 245(1) (2008), pp. 30-58.
    • (2008) J. Differential Equations , vol.245 , Issue.1 , pp. 30-58
    • Brzeźniak, Z.1    van Neerven, J.M.A.M.2    Veraar, M.C.3    Weis, L.4
  • 14
    • 84871066331 scopus 로고
    • On the construction of kernels. Séminaire de Probabilités IX
    • R.K. Getoor, On the construction of kernels. Séminaire de Probabilités IX, Lecture Notes in Math. 465 (1979), pp. 443-463.
    • (1979) Lecture Notes In Math , vol.465 , pp. 443-463
    • Getoor, R.K.1
  • 15
    • 23044529155 scopus 로고    scopus 로고
    • A note on maximal inequality for stochastic convolutions
    • E. Hausenblas and J. Seidler, A note on maximal inequality for stochastic convolutions, Czechoslovak Math. J. 51(126) (2001), pp. 785-790.
    • (2001) Czechoslovak Math. J , vol.51 , Issue.126 , pp. 785-790
    • Hausenblas, E.1    Seidler, J.2
  • 16
    • 37749031469 scopus 로고    scopus 로고
    • Stochastic convolutions driven by martingales: Maximal inequalities and exponential integrability
    • E. Hausenblas and J. Seidler, Stochastic convolutions driven by martingales: Maximal inequalities and exponential integrability, Stoch. Anal. Appl. 26(1) (2008), pp. 98-119.
    • (2008) Stoch. Anal. Appl , vol.26 , Issue.1 , pp. 98-119
    • Hausenblas, E.1    Seidler, J.2
  • 18
    • 0003335723 scopus 로고
    • Numerical Solution of Stochastic Differential Equations
    • (New York), Springer-Verlag, Berlin
    • P. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Applications of Mathematics (New York), Vol. 23, Springer-Verlag, Berlin, 1992.
    • (1992) Applications of Mathematics , vol.23
    • Kloeden, P.1    Platen, E.2
  • 20
    • 0003023917 scopus 로고    scopus 로고
    • The Convenient Setting of Global Analysis
    • American Mathematical Society, Providence, RI
    • A. Kriegl and P. Michor, The Convenient Setting of Global Analysis, Mathematical Surveys and Monographs, Vol. 53, American Mathematical Society, Providence, RI, 1997.
    • (1997) Mathematical Surveys and Monographs , vol.53
    • Kriegl, A.1    Michor, P.2
  • 22
    • 47749086029 scopus 로고    scopus 로고
    • Approximation of expectation of diffusion processes based on Lie algebra and Malliavin calculus
    • Springer, Tokyo
    • Sh. Kusuoka, Approximation of expectation of diffusion processes based on Lie algebra and Malliavin calculus, in Advances in Mathematical Economics, Vol. 6, Springer, Tokyo, 2004, pp. 69-93.
    • (2004) Advances In Mathematical Economics , vol.6 , pp. 69-93
    • Kusuoka, S.1
  • 24
    • 60549114069 scopus 로고    scopus 로고
    • Existence and uniqueness of path wise solutions for stochastic integral equations driven by Lévy noise on separable Banach spaces
    • V. Mandrekar and B. Rudiger, Existence and uniqueness of path wise solutions for stochastic integral equations driven by Lévy noise on separable Banach spaces, Stoch. Stoch. Reports 78(4) (2006), pp. 189-212.
    • (2006) Stoch. Stoch. Reports , vol.78 , Issue.4 , pp. 189-212
    • Mandrekar, V.1    Rudiger, B.2
  • 25
    • 70350588962 scopus 로고    scopus 로고
    • Regular dependence on initial data for stochastic evolution equations with multiplicative Poisson noise
    • C. Marinelli, C. Prévôt, and M. Röckner, Regular dependence on initial data for stochastic evolution equations with multiplicative Poisson noise, J. Funct. Anal. 258(2) (2010), pp. 616-649.
    • (2010) J. Funct. Anal , vol.258 , Issue.2 , pp. 616-649
    • Marinelli, C.1    Prévôt, C.2    Röckner, M.3
  • 28
    • 19744369999 scopus 로고    scopus 로고
    • Diffusions, Markov Processes, and Martingales
    • Cambridge University Press, Cambridge
    • L.C.G. Rogers and D. Williams, Diffusions, Markov Processes, and Martingales, Cambridge Mathematical Library, Vol. 2, Cambridge University Press, Cambridge, 2000.
    • (2000) Cambridge Mathematical Library , vol.2
    • Rogers, L.C.G.1    Williams, D.2
  • 29
    • 29344444148 scopus 로고    scopus 로고
    • Stochastic integration with respect to compensated poisson random measures on separable Banach spaces
    • B. Rudiger, Stochastic integration with respect to compensated poisson random measures on separable Banach spaces, Stoch. Stoch. Reports 76(3) (2004), pp. 213-242.
    • (2004) Stoch. Stoch. Reports , vol.76 , Issue.3 , pp. 213-242
    • Rudiger, B.1
  • 32
    • 16244397357 scopus 로고    scopus 로고
    • A series approach to stochastic differential equations with infinite dimensional noise
    • O. van Gaans, A series approach to stochastic differential equations with infinite dimensional noise, Integral Equations Operator Theory 51(3) (2005), pp. 435-458.
    • (2005) Integral Equations Operator Theory , vol.51 , Issue.3 , pp. 435-458
    • van Gaans, O.1
  • 34
    • 37249075950 scopus 로고    scopus 로고
    • Term structures of implied volatilities: Absence of arbitrage and existence results
    • [34] M. Schweizer and J. Wissel, Term structures of implied volatilities: absence of arbitrage and existence results, Mathematical Finance 18, pp. 77-114.
    • Mathematical Finance , vol.18 , pp. 77-114
    • Schweizer, M.1    Wissel, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.