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On jump processes with drift

Seria
Rozprawy Matematyczne tom/nr w serii: 202 wydano: 1983
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Warianty tytułu
Abstrakty
EN

CONTENTS
0. Introduction...................................................................................5
  0.1. Notations and preliminary results..............................................7
Chapter 1. Jump processes with drift.................................................9
  1.1. Definition basic properties........................................................9
  1.2. Characteristics of j.p.d............................................................12
    1.2.1. Drift functions.....................................................................12
    1.2.2. Drift time distributions.........................................................15
    1.2.3. Jump distributions...............................................................15
    1.2.4. Jump times, regeneration functions....................................18
    1.2.5. Summary.............................................................................20
    1.2.6. Characteristics and transition probabilities.........................21
  1.3. Construction of j.p.d................................................................22
    1.3.1. Construction of the "embedded chain"................................22
    1.3.2. Construction of the j.p.d......................................................24
    1.3.3. Characterization of j.p.d.......................................................29
Chapter 2. Feller j.p.d. on the real line..............................................29
  2.1. Preparations.............................................................................30
  2.2. Certain one-dimensional j.p.d....................................................33
    2.2.1. Definition.............................................................................33
    2.2.2. Existence of special Feller j.p.d...........................................34
  2.3. Remarks. Discussion of results.................................................46
References........................................................................................50
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 202
Liczba stron
51
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCII
Daty
wydano
1983
Twórcy
Bibliografia
  • [1] W. Doeblin, Sur certain mouvements aleatoires discontinus, Scand. Actuar. 22 (1939), 211 -222.
  • [2] J. L. Doob, Stochastic processes, New York 1953 (Russian translation: Moscow 1956).
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  • [4] E. B. Dynkin, Theory of Markov processes (Russian), Moscow 1963.
  • [5] W. Feller, Zur Theorie der stochastischen Prozesse, Math. Annalen 113 (1937), 113-160.
  • [6] W. Feller, On second order differential operators, Ann. Math. 61 (2) (1955), 90-105.
  • [7] I. I. Gichman, A. V. Skorochod, Theory of random processes (Russian), Moscow 1971 (vol. I), 1973 (vol. II).
  • [8] N. Ikeda, S. Watanabe, On some relations between the harmonic measure and the Lévy measure for a certain class of Markov processes, J. Math. Kyoto Univ. 2 (1962), 79-95.
  • [9] N. Ikeda, M. Nagasawa, S. Watanabe, A construction of Marcov processes by piecing out, Proc. Jap. Acad. 42 (1966), 370-375.
  • [10] M. Jacobsen, A characterization of minimal jump processes, Z. Wkt. 23 (1972), 32-46.
  • [11] T. Komatsu, Markov processes associated with certain integro-differential operators, Osaka J. Math. 10 (1973), 271-303.
  • [12] V. S. Koroliuk, Boundary problems for compound Poisson processes (Russian), Kiev 1975.
  • [13] K. Kuratowski, Sur une généralisation de la notion d'homéomorphie. Fund. Math. 22 (1934), 206-220.
  • [14] K. Kuratowski, Topology, vol. I; New York and London 1966.
  • [15] H. Langer, A class of infinitesimal generators of one-dimensional Markov processes, J. Math. Soc. Japan 28 (2) (1976), 242-249.
  • [16] M. Loève, Probability theory, Princenton 1963 (Russian), Moscow 1962.
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  • [18] K. Parthasaraty, Probality measures on metric spaces, New York and London 1976.
  • [19] D. Revuz, Markov chains, Amsterdam 1975.
  • [20] M. Rosenblatt, Random processes, New York 1974.
  • [21] K. Sato, Integration of the generalized Kolmogoroff-Feller backward equations, J. Fac. Sci. Univ. Tokyo 9 (1) (1961), 13 - 27.
  • [22] K. Sato, Lévy measures for a class of Markov semigroups in one dimension, Trans. Amer. Math. Soc. 148 (1970), 211-231.
  • [23] S. A. Sawyer, A formula for semigroups, with an application to branching diffusion processes, Trans. Amer. Math. Soc. 152 (1970), 1-38.
  • [24] I. S. Shitomirski, Certain questions of the theory of jump processes with deterministic segments (Russian), Teor. Funkcii Funkcional. Anal, i Prim. (2) (1966), 116-127.
  • [25] A. V. Skorochod, Homogeneous Markov processes without discontinuities of second kind (Russian), Teor. verojat. 12 (1967), 258-278.
  • [26] A. V. Skorochod, Limit theorems for stochastic processes (Russian), Teor. verojat. 1 (1956), 289-319.
  • [27] E. Szpilrajn, The characteristic function of a sequence of sets and some of its applications, Fund. Math. 31 (1-938), 207-223.
  • [28] S. Watanabe, On discontinuous additive functionals and Lévy measures of a Markov process, Japan. J. Math. 34 (1964), 53-70.
Języki publikacji
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Identyfikator YADDA
bwmeta1.element.zamlynska-e2934aa1-4e3c-428f-b159-38959f62579f
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ISBN
83-01-02146-2
ISSN
0012-3862
Kolekcja
DML-PL
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