| Ichiba, T., Karatzas, I. and Prokaj, V., "Diffusions with Rank-Based Characteristics and Values in the Nonnegative Quadrant", Bernoulli. to appear |
BibTeX:
@article{1,
author = {Ichiba, T. and Karatzas, I. and Prokaj, V.},
title = {Diffusions with Rank-Based Characteristics and Values in the Nonnegative Quadrant},
journal = {Bernoulli},
note = {to appear},
eprint = {1202.0036}
}
|
| Prokaj, V. (2013), "Some Sufficient Conditions for the Ergodicity of the Lévy Transformation", In Séminaire de Probabilités XLV., pp. 93-121. Springer International Publishing. |
BibTeX:
@incollection{2,
author = {Vilmos Prokaj},
editor = {Donati-Martin, Catherine and Lejay, Antoine and Rouault, Alain},
title = {Some Sufficient Conditions for the Ergodicity of the Lévy Transformation},
booktitle = {Séminaire de Probabilités XLV},
publisher = {Springer International Publishing},
year = {2013},
pages = {93-121},
doi = {10.1007/978-3-319-00321-4_2},
eprint = {1206.2485}
}
|
| Prokaj, V. (2013), "The solution of the perturbed Tanaka--equation is pathwise unique", Ann. Probab.. Vol. 41(3B), pp. 2376-2400. |
| Abstract: The Tanaka equation $dX_t=\sign(X_t)dB_t$ is an example of a stochastic differential equation (SDE) without strong solution. Hence pathwise uniqueness does not hold for this equation. In this note we prove that if we modify the right hand side of the equation, roughly speaking, with a strong enough additive noise, independent of the Brownian motion $B$ then the solution of the obtained equation is pathwise unique. |
BibTeX:
@article{3,
author = {Prokaj, Vilmos},
title = {The solution of the perturbed Tanaka--equation is pathwise unique},
journal = {Ann. Probab.},
year = {2013},
volume = {41},
number = {3B},
pages = {2376--2400},
doi = {10.1214/11-AOP716},
eprint = {1104.0740}
}
|
| Fernholz, E.R., Ichiba, T., Karatzas, I. and Prokaj, V. (2013), "Planar diffusions with rank-based characteristics and perturbed Tanaka equations", Probability Theory and Related Fields. Vol. 156(1), pp. 343-374. |
BibTeX:
@article{4,
author = {Fernholz, E.~R. and Ichiba, T. and Karatzas, I. and Prokaj, V.},
title = {Planar diffusions with rank-based characteristics and perturbed Tanaka equations},
journal = {Probability Theory and Related Fields},
year = {2013},
volume = {156},
number = {1},
pages = {343--374},
doi = {10.1007/s00440-012-0430-7}
}
|
| Herczegh, A., Prokaj, V. and Rásonyi, M. (2013), "Diversity and no arbitrage", submitted to the Stoch. Anal. Appl.. |
BibTeX:
@article{5,
author = {Herczegh, A. and Prokaj, V. and Rásonyi, M.},
title = {Diversity and no arbitrage},
journal = {submitted to the Stoch. Anal. Appl.},
year = {2013},
eprint = {1301.4173}
}
|
| Prokaj, V., Rásonyi, M. and Schachermayer, W. (2011), "Hiding a constant drift", Ann. Inst. Henri Poincaré Probab. Stat.. Vol. 47(2), pp. 498-514. |
| Review: The authors consider the following question of Marc Yor: Let $B$ be a Brownian motion and $S_t=t+B_t$. Can one define an $\scr F^B$-predictable process $H$ such that the stochastic integral $H\cdot S$ is an $\scr F^H\cdot S$-Brownian motion? The main result of the paper is a partial answer to the above problem. The authors show that the above problem has a weak solution: Let $W$ be a standard Brownian motion and $(\scr F^W_t)_t\geq0$ its natural filtration. Then there exists an $(\scr F^W_t)_t\geq0$-Brownian motion $B$ and an $(\scr F^W_t)_t\geq0$-predictable process $H$ which takes values in $[-1,1]$ and such that $H\cdot S$ is an $(\scr F^H\cdot S_t)_t\geq0$-Brownian motion, where $T_t=B_t+t$. The authors give several additional results and a generalization of the above statement. In a more recent paper by two of the authors [V. Prokaj and W. Schachermayer, "Hiding a constant drift---a strong solution'', preprint, Illinois J. Math., to appear] a strong solution to the above question is given. |
BibTeX:
@article{6,
author = {Prokaj, Vilmos and Rásonyi, Miklós and Schachermayer, Walter},
title = {Hiding a constant drift},
journal = {Ann. Inst. Henri Poincaré Probab. Stat.},
year = {2011},
volume = {47},
number = {2},
pages = {498--514},
url = {http://projecteuclid.org/euclid.aihp/1300887279},
doi = {10.1214/10-AIHP363}
}
|
| Prokaj, V. and Torma, B. (2011), "Identification of almost unstable Hawkes processes", Publ. Math. Debrecen. Vol. 78(1), pp. 103-126. |
| Abstract: Self-exciting point processes, also called Hawkes processes are widely used to model credit events (defaults) on bond markets in financial mathematics. This is a point process whose intensity is defined via feedback mechanism the input of which is the past of the point process itself. The identification (calibration) of Hawkes processes is a hot research area. In this paper we consider Hawkes processes in which the feedback path is defined by a finite dimensional linear system. This feedback system is well-defined if the integral of the impulse response function of the feedback path is strictly less than one. We investigate the behavior of the Fisher information matrix of the (conditional) maximum-likelihood estimator when the system parameters approach the boundary of the stability domain. We calculate also the limit distribution of the appropriately rescaled intensity process. |
BibTeX:
@article{7,
author = {Prokaj, Vilmos and Torma, Balázs},
title = {Identification of almost unstable Hawkes processes},
journal = {Publ. Math. Debrecen},
year = {2011},
volume = {78},
number = {1},
pages = {103--126},
doi = {10.5486/PMD.2011.4637}
}
|
| Herczegh, A. and Prokaj, V. (2011), "Shadow price in the power utility case", Ann. Appl. Probab.. under review |
BibTeX:
@article{8,
author = {Herczegh, A. and Prokaj, V.},
title = {Shadow price in the power utility case},
journal = {Ann. Appl. Probab.},
year = {2011},
note = {under review},
eprint = {1112.4385}
}
|
| Prokaj, V. and Rásonyi, M. (2010), "Local and true martingales in discrete time", Teor. Veroyatn. Primen.. Vol. 55(2), pp. 398-405. |
| Review: Let $(\Omega ,\scrF,P)$ be a probability space, and let $( \scrG_n)_n\geq 0$ be a filtration such that each $\scr G_n$ is a $P$-complete sub-$ \sigma $-algebra of $\scrF$. Suppose $(S_n)_n\geq 0$ is a local martingale with respect to the filtration $(\scr G_n)$. Moreover, let $(Y_n)_n\geq 0$ be a $(\scr G)_n$-adapted $\BbbR$-valued process. The authors prove that if $ (S_n)_n\geq 0$ is an $\BbbR$-valued $P$-local martingale, then for each $\varepsilon >0$ there is a probability measure $Q$ such that $P\sim Q$, $\|P-Q\|\leq \varepsilon $, $(S_n)_n\geq 0$ is a $Q$-martingale and each $Y_n$ is $Q$-integrable. Here $\|\cdot \|$ is the total variation norm. There are in the literature some results related to this topic, and they are based on functional analysis; on the other hand the proof given here uses measurable selection techniques. |
BibTeX:
@article{9,
author = {Prokaj, Vilmos and Rásonyi, Miklós},
title = {Local and true martingales in discrete time},
journal = {Teor. Veroyatn. Primen.},
year = {2010},
volume = {55},
number = {2},
pages = {398--405},
doi = {10.4213/tvp4225}
}
|
| Prokaj, V. and Schachermayer, W. (2010), "Hiding a constant drift---a strong solution", Illinois J. Math.. Vol. 54(4), pp. 1463-1480 (2012). |
BibTeX:
@article{10,
author = {Prokaj, Vilmos and Schachermayer, Walter},
title = {Hiding a constant drift---a strong solution},
journal = {Illinois J. Math.},
year = {2010},
volume = {54},
number = {4},
pages = {1463--1480 (2012)},
url = {http://projecteuclid.org/euclid.ijm/1348505537}
}
|
| Gerencsér, Lá. and Prokaj, V. (2010), "Stability of a class of hybrid linear stochastic systems", IEEE Trans. Automat. Control. Vol. 55(5), pp. 1233-1238. |
BibTeX:
@article{11,
author = {Gerencsér, László and Prokaj, Vilmos},
title = {Stability of a class of hybrid linear stochastic systems},
journal = {IEEE Trans. Automat. Control},
year = {2010},
volume = {55},
number = {5},
pages = {1233--1238},
doi = {10.1109/TAC.2010.2042353}
}
|
| Gerencsér L and Prokaj V (2010), "Recursive Identification of Continuous--Time Linear Stochastic Systems---An Off--Line Approximation". |
BibTeX:
@misc{4,
author = {Gerencsér, László and Prokaj, Vilmos},
title = {Recursive Identification of Continuous--Time Linear Stochastic Systems---An Off--Line Approximation},
year = {2010},
note = {19-th International Symposium on Mathematical Theory of Networks and Systems (MTNS2010) Budapest, 5-9 July 2010}
}
|
| Márkus, L., Arató, N.M. and Prokaj, V. (2010), "Hierarchical Bayesian modelling of geographic dependence of risk in household insurance", In Advances in data analysis. Boston, MA, pp. 219-227. Birkhäuser Boston. |
BibTeX:
@incollection{13,
author = {Márkus, László and Arató, N. Miklós and Prokaj, Vilmos},
title = {Hierarchical Bayesian modelling of geographic dependence of risk in household insurance},
booktitle = {Advances in data analysis},
publisher = {Birkhäuser Boston},
year = {2010},
pages = {219--227},
doi = {10.1007/978-0-8176-4799-5_20}
}
|
| Prokaj, V. (2009), "Unfolding the Skorohod reflection of a semimartingale", Statist. Probab. Lett.. Vol. 79(4), pp. 534-536. |
| Abstract: It is well-known that the Skorohod reflection of a Wiener process is the absolute value of another Wiener process with finer filtration. In other words it can be unfolded to obtain a Wiener process. In this short note a similar statement is proved for continuous semimartingales. |
BibTeX:
@article{14,
author = {Prokaj, Vilmos},
title = {Unfolding the Skorohod reflection of a semimartingale},
journal = {Statist. Probab. Lett.},
year = {2009},
volume = {79},
number = {4},
pages = {534--536},
doi = {10.1016/j.spl.2008.09.029}
}
|
| Prokaj, V. (2009), "Proposal selection for MCMC simulation", In XIII International Conference on Applied Stochastic Models and Data Analysis (ASMDA) June 30- July 3, 2009, Vilnius Lithuania. |
BibTeX:
@inproceedings{15,
author = {Prokaj, Vilmos},
title = {Proposal selection for MCMC simulation},
booktitle = {XIII International Conference on Applied Stochastic Models and Data Analysis (ASMDA) June 30- July 3, 2009, Vilnius Lithuania},
year = {2009},
url = {http://www.vgtu.lt/leidiniai/leidykla/ASMDA_2009/PDF/03_sec_014_Prokaj_Proposal.pdf}
}
|
|
Gerencsér, L. and Prokaj, V. (2009), "Recursive Identification of Continuous-Time Linear Stochastic Systems - Convergence w.p.1 and in $L_q$", In European Control Conference 2009 ECC'09 23-26 August 2009, Budapest, Hungary., pp. 1209-1214.
[BibTeX] |
BibTeX:
@inproceedings{16,
author = {Gerencsér, László and Prokaj, Vilmos},
title = {Recursive Identification of Continuous-Time Linear Stochastic Systems - Convergence w.p.1 and in $L_q$},
booktitle = {European Control Conference 2009 ECC'09 23-26 August 2009, Budapest, Hungary},
year = {2009},
pages = {1209--1214}
}
|
| Prokaj, V. (2003), "A characterization of singular measures", Real Anal. Exchange. Vol. 29(2), pp. 805-812. |
| Review: Given $c\in\BbbR$ and a probability measure $\mu$ on $\Bbb R$, denote by $\scr T_c\mu$ the translated measure defined by $\scr T_c\mu(A)\coloneq\mu(A-c)$ for Borel sets $A$ in $\BbbR$. The author shows that $\mu$ is singular with respect to Lebesgue measure if and only if the set of those $c$ for which $\mu$ and $\scr T_c\mu$ are mutually singular is dense. Moreover, this turns out to be equivalent with the existence of a Borel set $A$ with $\mu(A)=1$ with a continuum of disjoint translates. Some applications to $\sigma$-porous sets [cf. J. Tkadlec, Real Anal. Exchange 9 (1983/84), no. 2, 473--482; MR0766073 (85m:26001)] and to thin sets [cf. U. B. Darji and T. Keleti, Proc. Amer. Math. Soc. 131 (2003), no. 8, 2598--2596 (electronic); MR1974660 (2004d:03100)] are indicated. The paper contains nice proofs based on elementary martingale theory associated with the Hellinger integral. It seems that the results and the proofs carry over to more general locally compact (abelian?) groups with a countable basis for the topology. |
BibTeX:
@article{17,
author = {Prokaj, Vilmos},
title = {A characterization of singular measures},
journal = {Real Anal. Exchange},
year = {2003},
volume = {29},
number = {2},
pages = {805--812},
url = {http://projecteuclid.org/euclid.rae/1149698543}
}
|
| Elekes, M., Keleti, T. and Prokaj, V. (2001), "The composition of derivatives has a fixed point", Real Anal. Exchange. Vol. 27(1), pp. 131-140. |
BibTeX:
@article{18,
author = {Elekes, Márton and Keleti, Tamás and Prokaj, Vilmos},
title = {The composition of derivatives has a fixed point},
journal = {Real Anal. Exchange},
year = {2001},
volume = {27},
number = {1},
pages = {131--140},
url = {http://projecteuclid.org/euclid.rae/1212763956}
}
|
| Prokaj, V. (2001), "On a construction of J. Tkadlec concerning $\sigma$-porous sets", Real Anal. Exchange. Vol. 27(1), pp. 269-273. |
BibTeX:
@article{19,
author = {Prokaj, Vilmos},
title = {On a construction of J. Tkadlec concerning $\sigma$-porous sets},
journal = {Real Anal. Exchange},
year = {2001},
volume = {27},
number = {1},
pages = {269--273},
url = {http://projecteuclid.org/euclid.rae/1212763966}
}
|
| Prokaj, V. (1999), "Monotone and discrete limits of continuous functions", Real Anal. Exchange. Vol. 25(2), pp. 879-885. |
BibTeX:
@article{20,
author = {Prokaj, Vilmos},
title = {Monotone and discrete limits of continuous functions},
journal = {Real Anal. Exchange},
year = {1999},
volume = {25},
number = {2},
pages = {879--885},
url = {http://projecteuclid.org/euclid.rae/1230995421}
}
|
| Prokaj, V. (1997), "A note on pointwise convergence", Acta Math. Hungar.. Vol. 75(1-2), pp. 161-164. |
BibTeX:
@article{21,
author = {Prokaj, Vilmos},
title = {A note on pointwise convergence},
journal = {Acta Math. Hungar.},
year = {1997},
volume = {75},
number = {1-2},
pages = {161--164},
doi = {10.1023/A:1006590919919}
}
|
| Prokaj, V. (1997), "Restrictions of self-adjoint partial isometries", Period. Math. Hungar.. Vol. 35(3), pp. 211-214. |
BibTeX:
@article{22,
author = {Prokaj, Vilmos},
title = {Restrictions of self-adjoint partial isometries},
journal = {Period. Math. Hungar.},
year = {1997},
volume = {35},
number = {3},
pages = {211--214},
doi = {10.1023/A:1004557518015}
}
|
| Prokaj, V. (1996), "On the extensions of suboperators", Period. Math. Hungar.. Vol. 32(3), pp. 213-217. |
BibTeX:
@article{23,
author = {Prokaj, Vilmos},
title = {On the extensions of suboperators},
journal = {Period. Math. Hungar.},
year = {1996},
volume = {32},
number = {3},
pages = {213--217},
doi = {10.1007/BF02109791}
}
|
| Prokaj, V. (1996), "A note on equal convergence", Acta Math. Hungar.. Vol. 73(1-2), pp. 155-158. |
BibTeX:
@article{24,
author = {Prokaj, Vilmos},
title = {A note on equal convergence},
journal = {Acta Math. Hungar.},
year = {1996},
volume = {73},
number = {1-2},
pages = {155--158},
doi = {10.1007/BF00058950}
}
|
|
Prokaj, V. and Sebestyén, Z. (1996), "On Friedrichs extensions of operators", Acta Sci. Math. (Szeged). Vol. 62(1-2), pp. 243-246.
[BibTeX] |
BibTeX:
@article{25,
author = {Prokaj, Vilmos and Sebestyén, Zoltán},
title = {On Friedrichs extensions of operators},
journal = {Acta Sci. Math. (Szeged)},
year = {1996},
volume = {62},
number = {1-2},
pages = {243--246}
}
|
|
Prokaj, V. and Sebestyén, Z. (1996), "On extremal positive operator extensions", Acta Sci. Math. (Szeged). Vol. 62(3-4), pp. 485-491.
[BibTeX] |
BibTeX:
@article{26,
author = {Prokaj, Vilmos and Sebestyén, Zoltán},
title = {On extremal positive operator extensions},
journal = {Acta Sci. Math. (Szeged)},
year = {1996},
volume = {62},
number = {3-4},
pages = {485--491}
}
|
|
Prokaj, V. (1995), "On uniqueness of extension of suboperators", Ann. Univ. Sci. Budapest. Eötvös Sect. Math.. Vol. 38, pp. 47-53.
[BibTeX] |
BibTeX:
@article{27,
author = {Prokaj, V.},
title = {On uniqueness of extension of suboperators},
journal = {Ann. Univ. Sci. Budapest. Eötvös Sect. Math.},
year = {1995},
volume = {38},
pages = {47--53}
}
|