References
- K. Bichteler, Stochastic integration and lp theory of semimartingales, Ann. Probab. 9(1) (1982), pp. 49–89. doi: 10.1214/aop/1176994509
- K. Burdzy, W. Kang and K. Ramanan, The Skorokhod problem in a time-dependent interval, Stoch. Process Appl. 119 (2009), pp. 428–452. Available at http://dx.doi.org/10.1016/j.spa.2008.03.001. MR 2493998 (2010e:60076)
- M. Davis, J. Obłój and P. Siorpaes, Pathwise stochastic calculus with local times, Ann. de l'IHP 54(1) (2018), pp. 1–21.
- H. Föllmer, Calcul d'Itô sans probabilités, Séminaire de Probabilités XV 80 (1981), pp. 143–150. doi: 10.1007/BFb0088364
- R.L. Karandikar, On pathwise stochastic integration, Stoch. Process Appl. 57(1) (1995), pp. 11–18. doi: 10.1016/0304-4149(95)00002-O
- M. Lemieux, On the quadratic variation of semimartingales, Master Thesis, The University of British Columbia, https://circle.ubc.ca/handle/2429/23964 (1983). Available at https://circle.ubc.ca/handle/2429/23964.
- D. Lepingle, La variation d'ordre p des semi-martingales, Z. Wahrscheinlichkeitstheorie verw. Gebiete 36 (1976), pp. 295–316. doi: 10.1007/BF00532696
- R.M. Łochowski, On a generalisation of the Hahn-Jordan decomposition for real càdlàg functions, Colloq. Math. 132 (2013), pp. 121–138. doi: 10.4064/cm132-1-10
- R.M. Łochowski, On pathwise stochastic integration with respect to semimartingales, Probab. Math. Statist. 34(1-2) (2014), pp. 23–43. doi: 10.7151/dmps.1160
- R.M. Łochowski, On a generalisation of the Banach Indicatrix Theorem, Colloq. Math. 148(2) (2017), pp. 301–313. doi: 10.4064/cm6583-3-2017
- R.M. Łochowski, A new inequality for the Riemann-Stieltjes integrals driven by irregular signals in Banach spaces, J. Inequal. Appl. 2018(20) (2018), pp. 1–20.
- R.M. Łochowski and R. Ghomrasni, Integral and local limit theorems for level crossings of diffusions and the skorohod problem, Electron. J. Probab. 19(10) (2014), pp. 1–33. Available at https://projecteuclid.org/euclid.ejp/1465065652.
- R.M. Łochowski and R. Ghomrasni, The play operator, the truncated variation and the generalisation of the Jordan decomposition, Math. Methods Appl. Sci. 38 (2015), pp. 403–419. Available at http://onlinelibrary.wiley.com/doi/10.1002/mma.3077/full. doi: 10.1002/mma.3077
- R.M. Łochowski and P. Miłoś, On truncated variation, upward truncated variation and downward truncated variation for diffusions, Stoch. Process Appl. 123 (2013), pp. 446–474. doi: 10.1016/j.spa.2012.08.007
- R.M. Łochowski, N. Perkowski and D. Prömel, A superhedging approach to stochastic integration, Stoch. Process. Appl. (2018).
- P.E. Protter, Stochastic integration and differential equations, 2nd ed., Applications of Mathematics. Stochastic Modelling and Applied Probability Vol. 21, Springer-Verlag, Berlin, 2004. MR 2020294 (2005k:60008).
- V. Vovk, Itô calculus without probability in idealized financial markets, Lith. Math. J. 55(2) (2015), pp. 270–290. doi: 10.1007/s10986-015-9280-1
- E. Wong and M. Zakai, On the convergence of ordinary integrals to stochastic integrals, Ann. Math. Statist. 36 (1965), pp. 1560–1564. doi: 10.1214/aoms/1177699916