Medvegyev Péter
http://medvegyev.uni-corvinus.hu/StochasticIntegration/
2020-06-20T21:25:07+02:00Medvegyev Péter
http://medvegyev.uni-corvinus.hu/StochasticIntegration/
http://medvegyev.uni-corvinus.hu/StochasticIntegration/lib/images/favicon.icotext/html2016-09-20T13:04:02+02:00Medvegyev PéterStochastic Processes
http://medvegyev.uni-corvinus.hu/StochasticIntegration/doku.php?id=ch1&rev=1474369442&do=diff1474369442
1. The definition of jump operation on page 4. is correct only when the function is right or left regular. If the function is just regular then of course the function can have in fact three jumps at any point. Two one sided jumps and the jump defined on page 4. Or one can even say that in this case one cannot define the concept jump and one should talk about discontinuity. The simplest way to fix the problem is that one can think about a jump at a point as a function of time and not just a numbe…text/html2012-06-19T16:39:05+02:00Medvegyev PéterIto's formula
http://medvegyev.uni-corvinus.hu/StochasticIntegration/doku.php?id=ch6&rev=1340116745&do=diff1340116745
1. In (6.6) one should change k by i.
2. On page 360. one should say that on the random interval up to the stopping time the Wiener process remains in a compact subset of U and not only in a bounded subset. The problem is that the function f and its derivative are unbounded in the origin.text/html2011-01-25T08:09:31+02:00Medvegyev PéterMartingale Representation
http://medvegyev.uni-corvinus.hu/StochasticIntegration/doku.php?id=5.5&rev=1295939371&do=diff1295939371
1. On page 328 one can state that in the Martingale Representation Theorem the stochastic base is generated by the filtration that is
2. On page 346 Theorem 5.49 Is incorrectly formulated. The last line of the Theorem is missing. The correct version is here: [Download]text/html2011-01-02T08:07:52+02:00Medvegyev PéterThe Structure of Local Martingles
http://medvegyev.uni-corvinus.hu/StochasticIntegration/doku.php?id=ch3&rev=1293952072&do=diff1293952072
1. On page 186. in the proof of Proposition 3.15. the usual way means that first one applies the Monotone Class Theorem to get the proposition for bounded X. Then one applies the bounded case for the cutted processes, where a cutted process is X whenever X is smaller than n otherwise it is n. Then one applies that the limit of measurable functions is measurable.text/html2011-01-02T07:42:13+02:00Medvegyev PéterProcesses with independent increments
http://medvegyev.uni-corvinus.hu/StochasticIntegration/doku.php?id=ch7&rev=1293950533&do=diff1293950533
1. On page 461 it is said that the convergence of the characteristic function implies the convergence in probability. To prove this one needs of course the independence of increments. The detailed reasoning is on pages 62-63.
2. Using the Lévy-Khintchine formula one can easily prove Proposition 1.114: If the jumps of a stochastically continuous process with independent increment are bounded then all the moments of the process are finite.[Download]