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Textbooks/Monographs 1.
Pilipenko, A. (2014): An introduction to
stochastic differential equations with reflection. Potsdam: Universitätsverlag, 2014. – ix,
75 S. graph. Darst. (Lectures in pure and applied
mathematics 1); ISSN
(print) 2199-4951; ISSN (online) 2199-496X ISBN 978-3-86956-297-1. 2.
Gusak, D., Kukush, A., Kulik, A., Mishura, Y. and Pilipenko A.
(2009): Theory of Stochastic Processes with Applications to Financial Mathematics
and Risk Theory Series: Problem Books in Mathematics, Springer, 375 p. 6
illus., Hardcover ISBN: 978-0-387-87861-4. 3.
Nischenko, I. and Pilipenko, A. (2009): Probability theory and Mathematical
Statistics. Collection of problems
for students of Kiev Polytechnic Institute, Kiev, “Polytechnika”.
– 80p. (in Ukrainian). 4.
Gusak, D., Kukush, A., Kulik, A., Mishura, Y. and Pilipenko, A.
(2008): Collection of problems on Theory of Stochastic Processes and its
Applications, Kiev, VPC “Kiev University”, 398 p. (in Ukrainian). 5.
Gusak, D., Kulik, A., Mishura, Y. and Pilipenko, A. (2008): Collection of problems on Theory of
Stochastic Processes and its Applications in Financial Mathematics and Risk
Theory, Kiev, VPC “Kiev University”,
287 p. (in Ukrainian).
6.
Globa, L.S., Dyadenko, O.M., Pilipenko, A, and
Skulysh, M.A. Mathematical methods of analysis and
control of telecommunication networks. Kiev, “Polytechnika”.
– 284p. (Ukrainian), 2017. Eds. A.A. Dorogovtsev, A. Kulik, A. Pilipenko, M.I. Portenko, A.N. Shiryaev. (Eds.)
Selected works of Anatolii V. Skorokhod,
2016, Springer International Publishing, 391 p., ISBN :
9783319285078. Articles in journals/contributions to books 1.
Kindermann
S., Pereverzyev Jr S., Pilipenko A. (2018) The
quasi-optimality criterion in the linear functional strategy. Inverse Problems. – Vol.
34. –No. 7. – 075001, p. 1-24. 2.
Pilipenko, A. and Proske, F.N. (2018) On
perturbations of an ODE with non-Lipschitz
coefficients by a small self-similar noise. Statistics & Probability Letters. Volume 132, January 2018, 62-73. 3.
Pilipenko, A. and Proske, F.N. (2018) On a Selection Problem for Small
Noise Perturbation in the Multidimensional Case. Stochastics and
Dynamics, v.18, no.6, 23 pages, doi
10.1142/S0219493718500454 4.
Iksanov, A., Pilipenko, A. and Samoilenko, I.
(2017) Functional limit theorems for the maxima of perturbed random walks and
divergent perpetuities in the M1 topology. Extremes. September 2017, Volume 20, Issue 3, 567–583. 5.
Pilipenko, A. (2017) A
functional limit theorem for excited random walks. Electronic Communications in Probability, vol. 22, paper no. 39, 9 pp. 6.
Pilipenko, A. and Khomenko, V. (2017)
On a limit behavior of a random walk with
modifications upon each visit to zero. Theory
of Stochastic Processes, vol. 22(38),
no.1, 71-80. 7.
Aryasova,
O. and Pilipenko, A. (2017) A representation for the derivative with respect to the initial data
of the solution of an SDE with a non-regular drift. North-Western European Journal of Mathematics, vol 3, 1-40. 8.
Mandrekar,
V. and Pilipenko, A. (2016) On a Brownian motion with a hard
membrane. Statistics and Probability
Letters, 113, 62-70. 9.
Bogachev,
V.I. and Pilipenko, A. (2016) Strong solutions to stochastic equations with a Levy noise
and a non-constant diffusion coefficient,
Doklady Mathematics, 94 (1), 438 – 440. 10.
Pilipenko,
A., Tantsiura, M. (2016) A limit theorem for
countable systems of stochastic differential equations. Ukrainian Math. Journ., vol. 68,
¹ 10, 1380 – 1402. 11.
Iksanov,
A. and Pilipenko, A. (2016) A functional limit
theorem for locally perturbed random walks. Probability and Math. Stat. Vol. 36, No.2, 353-368. 12.
Pilipenko,
A., Prykhodko, Yu. (2016) A limit theorem for
singular stochastic differential equations. Modern Stochastics: Theory and
Applications. Vol. 3, No. 3, 223-235. 13.
Bogachev, V.I. and Pilipenko, A. (2015):
Strong solutions to stochastic equations with Lévy
noise and a discontinuous drift coefficient, Doklady Mathematics, 92 (1), 471 – 475. 14.
Pilipenko, A. and Sakhanenko, L. (2015) On a limit
behavior of one-dimensional random walk with non-integrable
impurity. Theory
of Stochastic Processes, vol. 20(36),
no.2, 97 – 104. 15.
Pilipenko,
A. and Prykhodko, Yu. (2015): On a limit behavior of a sequence of Markov processes
perturbed in a neighborhood of a singular point, Ukrainian mathematical
journal, vol.67, No.4, 564 – 583. 16.
Pilipenko,
A. and Tantsiura M. (2014): On the strong existence and uniqueness to a solution of a
countable system of SDEs with measurable drift, Theory of Stochastic Processes, vol. 19(35), no.2, 52 – 63. 17.
Aryasova,
O. and Pilipenko, A. (2014): On differentiability
of stochastic flow for à multidimensional SDE with discontinuous drift. Electron. Commun. Probab.,
19, No. 45, 1 – 17. 18.
Fang, S. and Pilipenko,
A. (2014): Additive functionals and push forward measures under Veretennikov's flow. In:
Festschrift Masatoshi Fukushima: In
Honor of Masatoshi Fukushima's Sanju
(Interdisciplinary Mathematical Sciences), World Scientific,163 – 178. 19.
Bogachev
V., Pilipenko, A. and Shaposhnikov
A. (2014): Sobolev functions on
infinite-dimensional domains, Journal of
Mathematical Analysis and Applications, Volume 419,
Issue 2, 15 November, 1023 – 1044. 20.
Iksanov
A. and Pilipenko, A. (2014): On the maximum of a
perturbed random walk, Statistics &
Probability Letters, Volume 92,
September 2014, 168 – 172. 21.
Aryasova,
O. and Pilipenko, A. (2014): On differentiability
with respect to the initial data of a solution of an SDE with Lévy noise and discontinuous coefficients. Stochastics
An International Journal of Probability and Stochastic Processes: formerly Stochastics and Stochastics
Reports, 86(4),
643 – 654. 22.
Pilipenko,
A. and Prykhodko, Yu. (2014): Limit behavior of a
simple random walk with non-integrable jump from a
barrier, Theory of Stochastic Processes.
19(35), no.1, 52 – 61. 23.
Bogachev,
V., Pilipenko, A. and Rebrova,
E. (2013): Classes of functions of bounded variation on infinite-dimensional
domains. Dokl. Russian Acad. Sci. Vol. 451, No. 2, 127 – 131. 24.
Pilipenko,
A. (2013): On differentiability of stochastic reflecting flow with respect to
starting point, Communications on Stochastic Analysis,
vol. 7, No. 1, 17 – 37. 25.
Pilipenko,
A. and Cherdyntseva, V. (2013) Analysis of the
Buffer’s Increment for the Billing.
Bulletin of V.Karazin Kharkiv
National University, series «Mathematical modeling. Information technology.
Automated control systems», No. 1063,
issue 22, 137-143. 26.
Pilipenko,
A., Uryvskyi, L. and Trach,
B. (2013): Asymptotic properties of self-similar traffic models based on
discrete-time and continuous-time martingales, Telecommunication Sciences, ¹ 2, 19 – 21. 27.
Pilipenko,
A. (2012): On existence and properties of strong solutions of one-dimensional
stochastic equations with an additive Levy noise. Theory of Stochastic Processes,
18(34),
no.2, 77 – 82. 28.
Dolzhenko
M.N., Nosenko N.M., Globa
L.S., Pilipenko, A., Prykhodko
O.O. and Rudenko S.A. (2012): Patients’ prognosis after coronary artery bypass grafting. Medicines in Ukraine , ¹ 1 – 2 (9 - 10). – p. 33–39.
(in Ukrainian) 29.
Aryasova,
O. and Pilipenko, A. (2012): On properties of a
flow generated by an SDE with discontinuous drift. Electronic Journal of Probability,
v. 17, article 106, 1 – 20. 30.
Aryasova,
O. and Pilipenko, A. (2011): On the strong
uniqueness of a solution to singular stochastic differential equations. Theory
of Stochastic Processes, vol.17(33), N 2, 1 – 15. 31.
Pilipenko,
A. (2011): On properties of Brownian reflecting flow in a wedge, Theory of Stochastic Processes. – 17(33), no.1, 79 – 89. 32.
Pilipenko,
A. and Prykhodko, Yu. (2011): On a limit behavior
of symmetric random walks with membranes, Teor. Imovir. Mat. Stat.
No. 85, 84 – 94 (Ukrainian);
translation in Theory
Probab. Math. Statist.
No. 85 (2012). 33.
Pilipenko,
A. (2011): On the Skorokhod mapping for equations
with reflection and possible jump-like exit from a boundary, Ukrainian mathematical
journal, Volume 63, Issue
9, 1415 – 1432. 34.
Bogachev,
V., Korolev, A. and Pilipenko,
A. (2010): Non uniform averaging in
the ergodic theorem for stochastic flows, Doklady
Mathematics, vol. 81, no. 3,
422 – 425. 35.
Aryasova,
O. and Pilipenko, A. (2009): On simultaneous
hitting of membrane by two skew Brownian motions. Theory of Stochastic Processes,
vol. 15(31), N 1, 1 – 7. 36.
Aryasova,
O. and Pilipenko, A. (2009): On Brownian motion on
the plane with membranes on rays with a common endpoint. Random Oper. and Stoch.
Equ., Vol. 17, No.
2, 137 – 156. 37.
Pilipenko,
A. (2007): Liouville theorem and its
generalizations, Mathematics today (Matematika
Segodnya), vol. 13, 47 – 77 (in Russian). 38.
Pilipenko,
A. (2006): On the generalized differentiability with initial data of a flow
generated by a stochastic equation with reflection. (Ukrainian) Teor. Imovir. Mat. Stat.
No. 75 (2006), 127—139;
translation in Theory
Probab. Math. Statist.
No. 75 (2007), 147 – 160. 39.
Pilipenko,
A. (2006): Transformation of Gaussian measure by infinite-dimensional
stochastic flow, Random Oper.
and Stoch. Equ., vol.14,
No 3, 275 – 290. 40.
Pilipenko,
A. (2006): Functional central limit
theorem for flows generated by stochastic equations with reflection, Nonlinear Oscillations,
vol.9, ¹ 1, 85 – 97. 41.
Pilipenko,
A. (2006): Propagation of absolute
continuity by a flow generated by stochastic equation with reflection, Ukrainian mathematical
journal, vol.58, ¹ 12,
1663 – 1673. 42.
Pilipenko,
A. (2006): Support theorem on stochastic flows with interaction, Theory
of Stochastic Processes, vol. 12(28), No.1-2, 127 –
141. 43.
Pilipenko,
A. (2006): Measure-Valued Diffusions and Corresponding Evolutionary Flows, Doklady
Mathematics, vol. 73, No. 2,
245–247. 44.
Pilipenko,
A. (2005): Measure-valued diffusions and continual systems of interacting
particles in random media, Ukrainian mathematical
journal, 57(9), 1507 –
1521. 45.
Pilipenko,
A. (2005): Properties of the flows generated by stochastic equations with
reflection, Ukrainian
mathematical journal, ¹8,
p.1069-1078. 46.
Pilipenko,
A. (2005): Stochastic reflecting flows, Dopovidi
Nats. Akad. Nauk Ukraini, ¹10, 23 – 29
(in Russian). (English translation available at arXiv:0810.4644) 47.
Mohammed, S. and Pilipenko, A. (2005): Absolute continuity of stationary
measure-valued processes generated by stochastic equations with interaction, Theory of Stochastic Processes,
vol.11(27), issue 1-2, 96 – 111. 48.
Pilipenko,
A. (2004): Flows generated by stochastic equations with reflection, Random Oper.
and Stoch. Equ., Vol. 12,
No. 4, 389 – 396. 49.
Pilipenko,
A. (2003): Transformation of measures in infinite-dimensional
spaces by the flow induced by a stochastic differential
equation, Sbornik: Mathematics, 194:4,
551–573, (Matematicheski˘ı Sbornik 194:4 85–106). 50.
Pilipenko,
A. (2003): Approximation theorem for stochastic differential equations with
interaction. Random Oper.
and Stoch. Equ., Vol. 11,
No.3, 213 – 228. 51.
Pilipenko,
A. (2002): Stroock and Varadhan
theorem for flows generated by stochastic differential equations with
interaction, Ukrainian
mathematical journal, vol. 54,
¹2, 280 – 291. 52.
Pilipenko,
A. (2001): Smoothness of distribution for solutions of SDE's with
interaction, Theory of Stochastic Processes,
vol.7(23), no.
3-4, 113 – 117. 53.
Pilipenko,
A. (2001): Stationary measure-valued processes generated by a flow of
interacted particles, Ukrainian
Mathematical Congress, Proceedings, 123 – 130. 54.
Kulik,
A. and Pilipenko, A. (2000): Nonlinear
transformations of smooth measures on infinite-dimensional spaces, Ukrainian mathematical
journal, v.52, no.9, 1403 – 1431. 55.
Pilipenko,
A. (1999): The evolution of a system of particles and measure-valued
processes, Theory of Stochastic Processes,
vol. 5(21),
no.3-4, 188 – 197. 56.
Alexandrova,
D., Bogachev, V. and Pilipenko,
A. (1999): On the convergence in the variation norm for the images of
measures under differentiable mappings - C.R.Acad.Sci.Paris,
t.328, Seria
1, 1055 – 1060. 57.
Alexandrova,
D., Bogachev, V. and Pilipenko,
A. (1999): On the convergence of induced measures in variation, Sbornik: Mathematics, vol.190, no.9, 1229 – 1245. 58.
Pilipenko,
A. (1998): Convergence of random vectors distributions in variation.- Theory of Stochastic Processes,
vol. 4(20), no.1-2, 238 – 251. 59.
Pilipenko,
A. (1997): On existence and uniqueness for a solution of linear stochastic
differential equation with respect to a logarithmic process, Ukrainian mathematical
journal, v.49, no.6, 863 – 871. 60.
Pilipenko,
A. (1997): Anticipative analogues of diffusion processes, Theory
of Stochastic Processes, vol. 3(19), no.3-4, 363 – 372. 61.
Pilipenko,
A. (1996): About properties of stochastic differential operator constructed
by a group, Ukrainian
mathematical journal, vol. 48,
no.4, 563 – 568. 62.
Pilipenko,
A. (1995): On locality of operators defined on the spaces of square
integrated functions, Mathematics today (Matematika
Segodnya), vol. 10, 26 – 41 (in Russian). 63.
Pilipenko,
A. (1995): On local operators which are diagonal with respect to Hermite polynomial system, Ukrainian mathematical
journal, vol. 47, no.4,
555 – 561. 64.
Pilipenko,
A. (1995): On locality of the closure of differential operators, Theory
of Stochastic Processes, vol. 1(17), no.1, 95 – 101 (in Russian). |