Limit Theorems on Large Deviations for Markov Stochastic Processes
Springer (Verlag)
978-94-010-7325-7 (ISBN)
0.1 Problems on large deviations for stochastic processes.- 0.2 Two opposite types of behaviour of probabilities of large deviations.- 0.3 Rough theorems on large deviations; the action functional.- 0.4 Survey of work on large deviations for stochastic processes.- 0.5 The scheme for obtaining rough theorems on large deviations.- 0.6 The expression: k (?) S (?) is the action functional uniformly over a specified class of initial points.- 0.7 Chapters 3 – 6: a survey.- 0.8 Numbering.- 1. General Notions, Notation, Auxiliary Results.- 1.1. General notation. Legendre transformation.- 1.2. Compensators. Lévy measures.- 1.3. Compensating operators of Markov processes.- 2. Estimates Associated with the Action Functional for Markov Processes.- 2.1. The action functional.- 2.2. Derivation of the lower estimate for the probability of passing through a tube.- 2.3. Derivation of the upper estimate for the probability of going far from the sets
$$ {{/Phi }_{{{{x}_{0}};/left[ {0,T} /right]}}}/left( i /right),{{/bar{/Phi }}_{{{{x}_{0}};/left[ {0,T} /right]}}}/left( i /right) $$.- 2.4. The truncated action functional and the estimates associated with it.- 3. The Action Functional for Families of Markov Processes.- 3.1. The properties of the functional
$$ {{S}_{{{{T}_{1}},{{T}_{2}}}}}/left( /phi /right) $$.- 3.2. Theorems on the action functional for families of Markov processes in Rr. The case of finite exponential moments.- 3.3. Transition to manifolds. Action functional theorems associated with truncated cumulants.- 4. Special Cases.- 4.1. Conditions A – E of § 3.1. – § 3.3.- 4.2. Patterns of processes with frequent small jumps. The cases of very large deviations, not very large deviations, and super-large deviations.- 4.3. The case of very large deviations.- 4.4. Thecase of not very large deviations.- 4.5. Some other patterns of not very large deviations.- 4.6. The case of super-large deviations.- 5. Precise Asymptotics for Large Deviations.- 5.1. The case of the Wiener process.- 5.2. Processes with frequent small jumps.- 6. Asymptotics of the Probability of Large Deviations Due to Large Jumps of a Markov Process.- 6.1. Conditions imposed on the family of processes. Auxiliary results.- 6.2. Main theorems.- 6.3. Applications to sums of independent random variables.- References.
Reihe/Serie | Mathematics and its Applications ; 38 | Mathematics and its Applications ; 38 |
---|---|
Zusatzinfo | XVI, 176 p. |
Verlagsort | Dordrecht |
Sprache | englisch |
Maße | 155 x 235 mm |
Themenwelt | Mathematik / Informatik ► Informatik ► Theorie / Studium |
Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
Naturwissenschaften ► Physik / Astronomie ► Thermodynamik | |
ISBN-10 | 94-010-7325-2 / 9401073252 |
ISBN-13 | 978-94-010-7325-7 / 9789401073257 |
Zustand | Neuware |
Haben Sie eine Frage zum Produkt? |
aus dem Bereich