Аннотация:
Строится и исследуется фундаментальное решение задачи Коши для уравнения ∂u∂t+Au=f, где A – псевдодифференциальный оператор, символ которого представляет собой сумму однородных функций. Результаты применяются для аналитического построения разрывных марковских процессов.
Библиография: 42 названия.
Образец цитирования:
А. Н. Кочубей, “Параболические псевдодифференциальные уравнения, гиперсингулярные интегралы и марковские процессы”, Изв. АН СССР. Сер. матем., 52:5 (1988), 909–934; Math. USSR-Izv., 33:2 (1989), 233–259
Shiliang Zhao, Quan Zheng, “Uniform complex time heat Kernel estimates without Gaussian bounds”, Advances in Nonlinear Analysis, 12:1 (2023)
V. A. Litovchenko, “Pseudodifferential Local Interaction Equation for Moving Objects”, Diff Equat, 58:1 (2022), 44
Stéphane Menozzi, Xicheng Zhang, “Heat kernel of supercritical nonlocal operators with unbounded drifts”, Journal de l'École polytechnique — Mathématiques, 9 (2022), 537
Vladyslav Litovchenko, “The Cauchy problem and distribution of local fluctuations of one Riesz gravitational field”, Fract Calc Appl Anal, 25:2 (2022), 668
Tadeusz Kulczycki, Alexei Kulik, Michał Ryznar, “On weak solution of SDE driven by inhomogeneous singular Lévy noise”, Trans. Amer. Math. Soc., 375:7 (2022), 4567
Vladyslav Litovchenko, Efthymios G. Tsionas, “Pseudodifferential Equation of Fluctuations of Nonstationary Gravitational Fields”, Journal of Mathematics, 2021 (2021), 1
Tadeusz Kulczycki, Michał Ryznar, Paweł Sztonyk, “Strong Feller Property for SDEs Driven by Multiplicative Cylindrical Stable Noise”, Potential Anal, 55:1 (2021), 75
V. Litovchenko, “ON THE NATURE OF A CLASSICAL PSEUDODIFFERENTIAL EQUATION”, BMJ, 8:2 (2020), 83
Tadeusz Kulczycki, Michał Ryznar, “Semigroup properties of solutions of SDEs driven by Lévy processes with independent coordinates”, Stochastic Processes and their Applications, 130:12 (2020), 7185
Alexei M. Kulik, “On weak uniqueness and distributional properties of a solution to an SDE with α-stable noise”, Stochastic Processes and their Applications, 129:2 (2019), 473
Niels Jacob, Elian O. T. Rhind, Tutorials, Schools, and Workshops in the Mathematical Sciences, Open Quantum Systems, 2019, 77
L. Huang, S. Menozzi, E. Priola, “L estimates for degenerate non-local Kolmogorov operators”, Journal de Mathématiques Pures et Appliquées, 121 (2019), 162
Alexei Kulik, “Approximation in law of locally α-stable Lévy-type processes by non-linear regressions”, Electron. J. Probab., 24:none (2019)
Peng Jin, “On weak solutions of SDEs with singular time-dependent drift and driven by stable processes”, Stoch. Dyn., 18:02 (2018), 1850013
Victoria Knopova, Alexei Kulik, “Parametrix construction of the transition probability density of the solution to an SDE driven by α-stable noise”, Ann. Inst. H. Poincaré Probab. Statist., 54:1 (2018)
Tadeusz Kulczycki, Michal Ryznar, “Transition density estimates for diagonal systems of SDEs driven by cylindrical alpha-stable processes”, ALEA, 15:2 (2018), 1335
M. M. Osypchuk, “On some perturbations of a symmetric stable process and the corresponding Cauchy problems”, Theory Stoch. Process., 21(37):1 (2016), 64–72
Цитирование в формате AMSBIB
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