Stochastic Volterra integral equations and a class of first-order stochastic partial differential equations

References

• N. Agram, B. Øksendal and S. Yakhlef, New approach to optimal control of stochastic Volterra integral equations, Stochastics 91(6) (2019), pp. 873–894.
   Google Scholar
• O.E. Barndorff-Nielsen, F.E. Benth and A. Veraart, Ambit stochastics, Springer Verlag, 2018.
   Google Scholar
• F.E. Benth and H. Eyjolfsson, Simulation of volatility modulated Volterra processes using hyperbolic stochastic partial differential equations, Bernoulli 22(2) (2016), pp. 774–793.
   Web of Science ®Google Scholar
• F.E. Benth and H. Eyjolfsson, Representation and approximation of ambit fields in hilbert space, Stochastics 89(1) (2017), pp. 311–347.
   Web of Science ®Google Scholar
• F.E. Benth and P. Krühner, The stochastics of prices in commodity and energy markets – an infinite dimensional view, Book in preparation, 2022.
   Google Scholar
• M.A. Berger and J.M. Victor, Volterra equations with Itô integrals I, J. Integral Equ. 2 3 (1980), pp. 187–245.
   Google Scholar
• M.A. Berger and J.M. Victor, Volterra equations with Itô integrals II, J. Integral Equ. 2 4 (1980), pp. 319–337.
   Google Scholar
• C. Chong, Lévy-driven Volterra equations in space and time, J. Theor. Probab. 30(3) (2017), pp. 1014–1058.
   Web of Science ®Google Scholar
• W.G. Cochran, J.S. Lee and J. Potthoff”, Stochastic Volterra equations with singular kernels, Stoch. Process. Appl. 56(2) (1995), pp. 337–349.
   Web of Science ®Google Scholar
• L. Coutin and L. Decreusefond, Stochastic Volterra equations with singular kernels, In: A.B. Cruzeiro and J. Zambrini, eds., Stochastic analysis and mathematical physics, progress in probability. Birkhäuser, Boston, MA, 2001, pp. 39–50.
   Google Scholar
• L. Decreusefond, Regularity properties of some stochastic Volterra integrals with singular kernel, Poten. Anal. 16(2) (2002), pp. 139–149.
   Web of Science ®Google Scholar
• K.J. Engel and R. Nagel, One-parameter semigroups for linear evolution equations, Springer, Verlag, 1999.
   Google Scholar
• D. Filipović, Consistency problems for Heath–Jarrow–Morton interest rate models, Springer, Verlag, 2001.
   Google Scholar
• D. Filipović, S. Tappe and J. Teichmann, Jump-diffusions in hilbert spaces: Existence, stability and numerics, Stochastics 82(5) (2010), pp. 475–520.
   Google Scholar
• J. Gatheral, T. Jaisson and M. Rosenbaum, Volatility is rough, Quantit. Fin. 18(6) (2018), pp. 933–949.
   Web of Science ®Google Scholar
• G. Gripenberg, S. Londen, StaffansVolterra integral and functional equations, Cambridge University Press, 1990.
   Google Scholar
• E. Jaber, M. Larsson and S. Pulido, Affine Volterra processes, Ann. Appl. Probab. 29(5) (2019), pp. 3155–3200.
   Web of Science ®Google Scholar
• B. Øksendal and T.S. Zhang, The stochastic Volterra equation, In: D. Nualart and M.S. Solé, eds., Barcelona seminar on stochastic analysis: St. feliu de guíxols. Birkhäuser, Basel, 1993, pp. 168–202.
   Google Scholar
• E. Pardoux and P. Protter, Stochastic Volterra equations with anticipating coefficients, Ann. Probab. 18(4) (1990), pp. 1635–1655.
   Web of Science ®Google Scholar
• S. Peszat and J. Zabczyk, Stochastic partial differential equations with Lévy noise, Cambridge University Press, 2007.
   Google Scholar
• V. Pham and C. Chong, Volterra-type Ornstein-Uhlenbeck processes in space and time, Stoch. Process. Appl. 128(9) (2018), pp. 3082–3117.
   Web of Science ®Google Scholar
• P. Protter, Volterra equations driven by semimartingales, Ann. Probab. 13 (1985), pp. 519–530.
   Web of Science ®Google Scholar
• B. Sz-Nagy and C. Foiaş, Harmonic analysis of operators on hilbert space, North-Holland Pub. Co., 1970.
   Google Scholar
• S. Tappe, Some refinements of existence results for SPDES driven by wiener processes and Poisson random measures, Int. J. Stoch. Anal. 2012 (2012).
   Google Scholar
• S. Tehranchi, A note on invariant measures for HJM models, Fin. Stoch. 9(3) (2005), pp. 389–398.
   Web of Science ®Google Scholar
• Z. Wang, Existence and uniqueness of solutions to stochastic Volterra equations with singular kernels and non-Lipschitz coefficients, Stat. Probab. Lett. 78(9) (2008), pp. 1062–1071.
   Web of Science ®Google Scholar
• X. Zhang, Stochastic Volterra equations in Banach spaces and stochastic partial differential equation, J. Funct. Anal. 258(4) (2010), pp. 1361–1425.
   Web of Science ®Google Scholar